Solving_the_Schrodinger_Equation_Numerically.ipynb

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      "source": [
        "# Numerically Solving the Schrödinger Equation\n",
        "(Some of the following (mostly, I think, the finite differences procedure) was taken from someone else's Jupyter notebook and I can't remember whose. Credit to that unknown creator.)\n",
        "\n",
        "The number of problems for which we will be able to find an analytical solution to the Schrödinger equation is limited. We have seen how to solve the particle in a box and we will be able to analytically solve some others but even in those cases we often rely on solutions by long dead French mathematicians rather than doing the tedious work ourselves.\n",
        "\n",
        "We should use the cases in which we can find a precise solution to develop our intuition about what a reasonable solution looks like and be able to make informed qualitative guesses at what a good wavefunction will be. But it would also be useful to know techniques in calculating the wavefunctions and energies numerically. Here our answers may not be precise but we with enough work we should be able to approach the true answer as closely as we want.\n",
        "\n",
        "We have seen the Schrödinger Equation written as a differential equation and we have seen that it forms an eigenfunction/eigenvalue equation.\n",
        "$$ -\\frac{\\hbar^2}{2m}\\frac{d^2}{d x^2} \\psi(x) + V(x)\\psi(x) = E\\psi(x)$$\n",
        "\n",
        "Here we will see how to transform the equation into a matrix equation that preserves the eigenfunction/eigenvalue form (where the term $eigenfunction$ is replaced by $eigenvector$).\n"
      ]
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      "source": [
        "## Method\n",
        "The method we will use here is called the [\"Finite Difference Method\"](https://en.wikipedia.org/wiki/Finite_difference_method) (see the linked Wikipedia article). In this method we will turn the function $\\psi(x)$ into a vector, which is a list in Python, and the operator of the differential equation into a *matrix*. We then end up with a matrix eigenequation, which we can diagonalize to get our answer.\n",
        "\n",
        "### Discretization\n",
        "The process of discretization is simply turning our continuous space $x$, into a discrete number of steps, $N$, and our function $\\psi(x)$ into an array of size $N$. We thus have $N$ values $x_i$, which have a stepsize $h = \\Delta x = x_{i+1} - x_i$. Our choice of the *size* of our space, $N$, turns out to be important. Too large a number will slow down our computation and require too much computer memory, too small a number and the answers we compute will not be sufficiently accurate. A common practice is to start with a small number $N$ and then increase it until the accuracy is acceptable. The actual value you obtain in the end will depend on the problem you are studying.\n",
        "\n",
        "### first order differential\n",
        "We first need to develop how we will take the derivative of our function. Going back to our introduction to calculus, we remember that the derivative was defined as:\n",
        "$$\n",
        "\\frac{d}{dx} f(x) = \\lim_{\\Delta x \\rightarrow 0} \\frac{f(x+\\Delta x) - f(x)}{\\Delta x} \\approx \\frac{f(x+h) - f(x)}{h} + \\mathrm{O}(h)\n",
        "$$\n",
        "When we take a *finite difference*, we simply not take the limit all the way down to 0, but stop at $\\Delta x = h$. Note that for this equation we evaluate the point just *after* $x$, which we call the *forward difference*. There are other possible ways to do a finite difference but we won't concern ourselves with them here.\n",
        "\n",
        "Note that for this approximation to a derivative, we have a problem at the end of our space. In our case, $x+\\Delta x$ is not defined at the last point. To account for this, we'll have to ignore the last point of our derivative."
      ]
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      "source": [
        "#### Matrix representation\n",
        "Matrix and vector methods are very straightforward to implement using a computer. We need to see how a matrix can be setup to take a derivative. I expect that many of you will not have taken linear algebra and we won't need to concern ourselves too much with each detail of the matrix but you should be able to see the main point. You can look at the[ matrix multiplication section ](#scrollTo=xsj8ZRIiPpNr&line=10&uniqifier=1)to get a little background that may be useful.\n"
      ]
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      "cell_type": "markdown",
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      "source": [
        "We'll want to find a matrix that can turn our vector representation of $\\psi$ into its derivative.\n",
        "We now want to turn our Schrödinger equation into a matrix equation for us to evaluate. If you just want to take the derivative of a function stored in an array, then this is not needed, you can run a loop and evaluate the equation for each $x_i$, but if you want to solve a differential equation, we need the matrix.\n",
        "\n",
        "We introduce the vectors $f(x) = [f_0,f_1,f_2,...,f_{N-1}]$ and for the derivative $f'(x) = [f'_0,f'_1,f'_2...,f'_{N-1}]$. The forward difference derivative can then be written as:\n",
        "$$ f'_i = (f_{i+1} - f_i)/h $$\n",
        "And the matrix equation for the forward difference derivative is just:\n",
        "$$\n",
        "\\begin{pmatrix}f'_0 \\\\ f'_1 \\\\\\vdots \\\\ f'_{N-1}\\end{pmatrix} = \\frac{1}{h}\\begin{pmatrix}f_1-f_0\\\\f_2-f_1\\\\\\vdots\\\\f_{N}-f_{N-1}\\end{pmatrix}= \\frac{1}{h}\n",
        "\\begin{pmatrix} -1 & 1 & 0 & & \\\\ 0 & -1 & 1 & & \\\\ & & \\ddots & \\ddots \\\\\n",
        "& & & -1 & \\end{pmatrix}\\begin{pmatrix}f_0 \\\\ f_1 \\\\\\vdots \\\\ f_{N-1}\\end{pmatrix}\n",
        "$$\n",
        "\n",
        "The matrix only has two non-zero elements on each row. This means that only the two corresponding elements in the function vector ($f_0$, $f_1$, $f_2$, $f_3$ ...) will be affected by the multiplication of each row. So, ignoring the division by $h$, the first row of the resulting vector will be $-1\\cdot f_0 + 1\\cdot f_1 + 0\\cdot f_2 + 0\\cdot... = f_1-f_0$\n",
        "\n",
        "We note that the last entry in the matrix will not be correct because there is no element for $N$. We will need to remember to ignore this last point in our calculation of the derivative.\n",
        "\n",
        "So the multiplication of the derivative matrix by our function returns the difference between each adjacent point in our function. After this the derivative is obtained by dividing each element by the difference between each point on the $x$-axis, here denoted by $h$. As long as this distance is constant, we can simply divide each element by $h$ to get the derivative.\n",
        "\n",
        "We now check that this works. Using Python and Numpy we will take the derivative of $\\sin(x)$ and plot the result.\n",
        "First we tell the system we want to use the Numpy package to deal with numerical calculations and the matplotlib package to deal with making plots.\n",
        "Then setup some parameters such as number of points, the $x$-axis range, etc."
      ]
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      "source": [
        "### Example derivative calculation\n",
        "#### Small matrices\n",
        "We'll calculate the derivative using a matrix like the one above of $y=2x$ over some small range of $x$ as a way of testing the technique while using functions for which we can easily see whether the technique is working."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np # import numerical computation functions\n",
        "import matplotlib.pyplot as plt # import plotting functions"
      ],
      "metadata": {
        "id": "UMQrYYJa3V5E"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "N=6 # chop the x domain in to N pieces. Keep it small for fast calculations, large for more accuracy\n",
        "x=np.linspace(0,5,N) # set up the array of x values. Begin at the first number, end at the second value, and return N evenly spaced numbers.\n",
        "\n",
        "Δx = x[1]-x[0] # name a variable for the spacing between the x values"
      ],
      "metadata": {
        "id": "4o1i5usL4Eh0"
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      "execution_count": 2,
      "outputs": []
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      "cell_type": "markdown",
      "source": [
        "We can use generate our matrix using the numpy [diag and ones](#scrollTo=5W2m_ana1yrl&line=2&uniqifier=1) functions"
      ],
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      "source": [
        "D=(np.diag(-1*np.ones(N),0)+np.diag(np.ones(N-1),1))/Δx #define derivative matrix put -1 on the diagonal and 1 on the at all points just above the diagonal\n",
        "\n",
        "y=2*x # this is the function we want to differentiate\n",
        "yprime=D@y #matrix multiply D and y. D.dot(y) or np.matmul(D,y) also accomplishes the multiplication. D*y does not.\n",
        "yprime=yprime[:-1] # :-1 means exclude the last point as there is no point f(x+Δx) to evaluate.\n",
        "\n",
        "print(\"The derivative is \",yprime)\n",
        "\n",
        "plt.plot(x,y,label='y(x)')\n",
        "plt.plot(x[:-1],yprime,label='dy/dx)')  # we have to leave off the last element of x to make it the same size as the derivative.\n",
        "                                        #Leave off [:-1] here and in yprime definition to see what happens if you keep all the points.\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n"
      ],
      "metadata": {
        "id": "Io8fJ8S24ZCK"
      },
      "execution_count": null,
      "outputs": []
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      "cell_type": "markdown",
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      "source": [
        "You should see that the derivative is a constant, 2.\n",
        "\n",
        "Try changing $y(x)$ to $x^2$ (which you express in python as ```x**2```). The derivative here should still be linear but with a non-zero slope.\n",
        "\n",
        "Try $y(x)=x^3$. You should notice that the curves are made up of line segments. Increasing the value of $N$ will create smoother curves and a more accurate derivative. Try N=50.\n",
        "\n",
        "Now try $y(x)=sin(x)$. Type ```np.sin(x)``` to get the $sin$ function since it comes from the numpy library."
      ]
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      "source": [
        "### Second order Differential\n",
        "We can now extend this method to the second order differential. Since we did a 'forward' first derivative (adding Δx), it will be convenient for us to do a ['backward'](#scrollTo=DkcuHT4C-bpw&line=2&uniqifier=1) second derivative here:\n",
        "$$\n",
        "\\frac{d^2}{dx^2}f(x) = \\lim_{\\Delta x \\rightarrow 0} \\frac{f'(x)-f'(x-\\Delta x)}{\\Delta x} =  \\lim_{\\Delta x \\rightarrow 0} \\frac{f(x+\\Delta x) - f(x) - (f(x) - f(x-\\Delta x))}{\\Delta x^2} \\\\\n",
        "\\frac{d^2}{dx^2}f(x) = \\lim_{\\Delta x \\rightarrow 0} \\frac{f(x+\\Delta x) - 2f(x) + f(x-\\Delta x))}{\\Delta x^2} \\approx \\frac{f(x+\\Delta x) - 2f(x) + f(x-\\Delta x))}{\\Delta x^2}\n",
        "$$\n",
        "So in the discrete space we can write this as:\n",
        "$$ f''_i = (f_{i+1} - 2f_i + f_{i-1})/\\Delta x^2 $$\n",
        "And finally, as a matrix equation, the second derivative is then:\n",
        "$$\n",
        "\\begin{pmatrix}f''_0 \\\\ f''_1 \\\\ f''_2 \\\\\\vdots \\\\ f''_{N-1}\\end{pmatrix} = \\frac{1}{\\Delta x^2}\n",
        "\\begin{pmatrix} -2 & 1 & 0 & 0 & \\\\ 1 & -2 & 1 & 0 & \\\\\n",
        "0& 1 & -2 & 1 &  \\\\ &  & \\ddots & \\ddots & \\ddots &\\\\\n",
        "&  & & 1 & -2 \\end{pmatrix}\\begin{pmatrix}f_0 \\\\ f_1 \\\\ f_2 \\\\\\vdots \\\\ f_{N-1}\\end{pmatrix}\n",
        "$$\n",
        "Where now we note that at both ends of our array we will get an inaccurate answer unless we do some fixup. The fixup in this case is to use the same elements as the row below (at the start) or the row above (at the end), so we get $f''_0 = f''_1$ and $f''_{N-1} = f''_{N-2}$, which is not great but better than the alternative.\n",
        "\n",
        "We can now try this matrix in Python and compute the second derivative of our $y(x)$ array."
      ]
    },
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      "cell_type": "code",
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      "source": [
        "N=200\n",
        "x=np.linspace(0,2*np.pi,N)\n",
        "Δx=x[1]-x[0]\n",
        "\n",
        "y=np.sin(x)\n",
        "\n",
        "D1=(np.diag(-1*np.ones(N),0)+np.diag(np.ones(N-1),1))/Δx\n",
        "\n",
        "D2 = (np.diag(np.ones(N-1),-1) + np.diag( -2.*np.ones(N),0) + np.diag(np.ones(N-1),1))/(Δx**2)\n",
        "                # The first np.diag() puts (N-1) ones on the partial diagonal below the diagonal (,-1)\n",
        "                # The second puts N negative twos on the diagonal. The third puts (N-1) ones on the partial diagonal above the diagonal (,1).\n",
        "yp=D1.dot(y) # take derivative so we can use it in our plot\n",
        "ypp = D2.dot(y) # take second derivative of function, y.\n",
        "\n"
      ],
      "execution_count": 4,
      "outputs": []
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      "cell_type": "markdown",
      "source": [
        "At this point we have the first and second derivatives. Let's plot them."
      ],
      "metadata": {
        "id": "8F5g1M5xZrRT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10,7))\n",
        "plt.plot(x,y,label='y(x)',color='blue')\n",
        "plt.plot(x[:-1],yp[:-1],label='y\\'(x)',color='orange')     # Last value is invalid, don't plot\n",
        "plt.plot(x[1:-1],ypp[1:-1],label='y\\'\\'(x)',color='green')  # First and last value is invalid.\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "Yog1BZMcZqcv"
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      "execution_count": null,
      "outputs": []
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      "cell_type": "markdown",
      "source": [
        "Do these derivatives of sine lead to the result you expect?"
      ],
      "metadata": {
        "id": "Jee2_7sfaO3_"
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      "cell_type": "markdown",
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      "source": [
        "# Solving the Particle in a Box Schrödinger Equation\n",
        "\n",
        "We can now setup the Schrodinger Equation as a matrix equation:\n",
        "$$\n",
        "\\hat H = \\frac{\\hbar^2}{2m}\\frac{d^2}{d x^2} + V \\\\\n",
        "\\hat H \\psi(x) = E \\psi(x)\n",
        "$$\n",
        "We now know the matrix for taking the second order derivative. The matrix for the potential is simply the values of the potential on the diagonal of the matrix: $\\mathbf{V}_{i=j} = V_i$. The result of multiplying the function vector will be to simply multiply each element of the function by the value of the potential.\n",
        "\n",
        "Writing out the matrix for $\\mathbf{H}$ we get:\n",
        "$$\n",
        "\\mathbf{H} = \\frac{-\\hbar^2}{2 m \\Delta x^2} \\begin{pmatrix} -2 & 1 & 0 & 0 & \\\\ 1 & -2 & 1 & 0 & \\\\\n",
        "0& 1 & -2 & 1 &  \\\\ &  & \\ddots & \\ddots & \\ddots &\\\\\n",
        "&  & & 1 & -2 \\end{pmatrix} +\n",
        "\\begin{pmatrix} V_0 & 0 & 0 & & \\\\ 0 & V_1 & 0 & & \\\\ 0 & 0 & V_2 & & \\\\ & & &\\ddots & \\\\ &&&&V_{N-1}\\end{pmatrix}\n",
        "$$\n",
        "\n",
        "It is worth looking at the matrix of the Hamiltonian and notice the symmetry: $\\mathbf{H}^T = \\mathbf{H}$, so the transpose of the matrix is identical to the matrix. Since the matrix is *real* everywhere, the complex conjugate is also the same: $\\mathbf{H}^*=\\mathbf{H}$. Combining these two statements, we can say that the Hamiltonian is Hermetian: $\\mathbf{H}^\\dagger = \\mathbf{H}$.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "waZQcEJ2Gpbo"
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      "source": [
        "### Infinite Square Well\n",
        "The very simplest system to solve for is the infinite square well, for which $V=0$. We will readily recognize the results as alternating $\\cos(x)$ and $\\sin(x)$ functions, and the energy levels are:\n",
        "$$\n",
        "E_i = \\frac{n^2\\pi^2\\hbar^2}{2ma^2}\n",
        "$$\n",
        "First, we need to discuss a subtlety. The Infinite Square Well from $-a/2$ to $a/2$ has $V=\\infty$ *at* these points. We get into trouble trying to enter $\\infty$ in our potential, so what we need to do is just limit the computational space from $-a/2+h$ to $a/2-h$, where $h$ is our step size. That way we force the wavefunction to zero at the end points.\n",
        "We compute this in the next box. I create $x_{full}$ as the full x-axis from $-a/2$ to $a/2$, but take $N+2$ steps. I then leave out the first and last point when calculating the wavefunctions. At the end, before plotting, I add a zero to the beginning and end of the wavefunctions, so that we get the expected result for plotting.\n",
        "\n",
        "Note I again import everything and setup all the definitions, so this block is stand-alone, and can be copy-pasted into another notebook. Here we set up constants and import the library needed for dealing with linear algebra."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IhNgMM2JwqbN"
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      "source": [
        "hbar=1 # use atomic units\n",
        "m=1 # electron mass\n",
        "\n",
        "N = 1000\n",
        "a = 1.0 # this doesn't matter unless we want to compare different size boxes.\n",
        "x = np.linspace(-a/2.,a/2.,N)\n",
        "\n",
        "Δx = x[1]-x[0] # This is the difference between points.\n",
        "\n",
        "nl= 8 # the number of levels to calculate. Change this as you wish."
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S3BD4pgiw61b"
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      "source": [
        "Now we set up the potential energy, the second derivative operator, and the Hamiltonian. Then extract the eigenvalues and eigenfunctions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NSQlwgwp7WUr"
      },
      "source": [
        "V = 0.*x # could be just zero but put x here to show that it is a function of x.\n",
        "D2 = 1./(Δx**2)*(np.diag(np.ones(N-1),-1) -2* np.diag(np.ones(N),0) + np.diag(np.ones(N-1),1)) # derivative operator\n",
        "H = -(hbar*hbar)/(2.0*m)*D2 + np.diag(V)  # Hamiltonian including derivative and potential energy.\n",
        "\n",
        "\n",
        "E,psiT = np.linalg.eigh(H) # This computes the eigenvalues and eigenvectors\n",
        "psi = np.transpose(psiT)   # We take the transpose of psiT to the wavefunction vectors can accessed as psi[n]"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MMLJfLqXy-8P"
      },
      "source": [
        "The energies are stored in $E$. The first $N$ levels are calculated. We will focus on only a few of them. Let's list the first several in atomic energy units."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BaT2X-RyzHBa"
      },
      "source": [
        "for i in range(nl):\n",
        "  print(\"E_{}={:8.3f}\".format(i+1,E[i])) # the notation here is strange. Basically we will print everything between the \"\"\n",
        "                                         #but stuff between the brackets will get subsitututed in from the between the parentheses in .format()\n",
        "                                         #So here we'll print i+1 which is the quantum number 'n' in the particle in a box and the energies.\n",
        "                                         #The :8.3f stuff indicates how many places to use for the whole number (some may be spaces) and how many for the\n",
        "                                         #after the decimal point. The 'f' indicates a floating point (or decimal number). If we don't care about the\n",
        "                                         #format of the number that is displayed or if the number is a whole number as it is, like 'i', just {} is fine."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tgmSRoMdz22k"
      },
      "source": [
        "####Scaling the energies\n",
        "The energy of the lowest level in a particle in a box is $\\frac{n^2 \\hbar^2 \\pi^2}{2 m a^2}$. For convenience we will rescale the energies to be relative to the energy of the first level. So $\\epsilon=\\frac{E_n}{E_1}=\\frac{E_n}{\\frac{\\hbar^2 \\pi^2}{2ma^2}}=\\frac{E_n}{\\frac{\\pi^2}{2}}=\\frac{2E_n}{\\pi^2}$ and $ϵ=\\frac{E_n}{\\frac{\\hbar^2 \\pi^2}{2ma^2}}=\\dfrac{\\frac{n^2 \\hbar^2 \\pi^2}{2ma^2}}{\\frac{\\hbar^2 \\pi^2}{2ma^2}}=n^2$. So we can rescale the energy by dividing by $\\pi^2/2$ and the resulting value should be the quantum number squared. This makes it easy to see at a glance how close our numerical approximate answer is the analytical answer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YRLYrQ4cz2RU"
      },
      "source": [
        "ϵ=[E[i]/(hbar**2*np.pi**2/(2*m*a**2)) for i in range(nl)] # we only need divide by pi**2/2 but hbar, m, and a are set equal to 1 so...\n",
        "for i in range(nl):\n",
        "  print(\"ϵ_{}={:>8.3f}\".format(i+1,ϵ[i]))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9w5UfASV7jNQ"
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      "source": [
        "Our calculation gives almost what we expect. Each energy is essentially $n^2$ as it should be. If you change $N$ above and re-run the cells, you can see what affect using fewer (or more) points will have on runtime and accuracy. Try N=100 and N=5000. Remember that our calculation uses an N by N matrix so N=5000 will have to deal with a 25,000,000 element matrix."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uN1rea9O7WVa"
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      "source": [
        "We now want to plot the wavefunctions. We can plot individual wavefunctions using matplotlib (abbreviated as $plt$) and the $x$ and $psi$ lists we made above. For instance,\n",
        "```\n",
        "plt.plot(x,psi[2])\n",
        "```\n",
        "will the wavefunction corresponding to $n=3$ (remember we start counting at 0, so $n=1$ corresponds to psi[0]).\n",
        "\n",
        "Try plotting several of the wavefunctions below. Do they match what you think they should look like?\n",
        "\n",
        "You can beautify your graphs by adding axis labels and a title.\n",
        "\n",
        "```\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('$\\psi$')\n",
        "plt.title('Particle in an infinite box wavefunction')\n",
        "```\n",
        "If you just type the lines shown here, some strange symbols will appear above the graph. Use ```plt.show()``` at the end and these go away.\n",
        "\n",
        "Now we normalize the eigenvectors. To do this we take the integral $\\int^∞_{-\\infty}A^*\\psi ^*A\\psi dx=1$ where $A$ is the normalization constant. Solving for $A$ gives $$A=\\dfrac{1}{$\\int^∞_{-\\infty}\\psi ^*\\psi dx=1} $$. In numpy, we can use the trapezoidal integration function, ```trapz``` to do the integration."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gvPgLIxa8_26"
      },
      "source": [
        "norm=[np.sqrt(1/np.trapz(psi[i]**2,x)) for i in range(nl)] # calculate normalization for each eigenfunction\n",
        "psi_norm=[psi[i]*norm[i] for i in range(nl)] # normalize psi"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dKxs4umR8oxZ"
      },
      "source": [
        "We'll set up a mechanism to plot a bunch of wavefunctions at the same time.\n",
        "\n",
        "The sign of the wavefunctions as we approach the ends is arbitrary. We can make it consistent if we want. The $for$ loop below plots each wavefunction but it also makes it so that the left end points all approach zero from above. The right end points then alternate."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HTkwSuQw7WVs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        },
        "outputId": "825db98d-4d5f-4d21-9535-f5a601d91da8"
      },
      "source": [
        "plt.figure(figsize=(10,7))\n",
        "fact=0.05 # scale for plotting\n",
        "for i in range(1,nl+1): # start with i=1 and go to i=\n",
        "  if psi_norm[i-1][10] < 0:   # Flip the wavefunctions if it is negative at large x, so plots are more consistent.\n",
        "      plt.plot(x,-psi_norm[i-1]/np.sqrt(Δx)*fact+ϵ[i-1],label=\"$ϵ_{}$={:>8.3f}\".format(i,ϵ[i-1]))\n",
        "  else:\n",
        "      plt.plot(x,psi_norm[i-1]/np.sqrt(Δx)*fact+ϵ[i-1],label=\"$ϵ_{}$={:>8.3f}\".format(i,ϵ[i-1]))\n",
        "plt.title(\"Eigenfunctions of the Infinite Square Well\")\n",
        "V_x = np.zeros([N],float) # potential energy is just zeros. We don't need it for calculating but we do for plotting\n",
        "for i in range(N): # but adjust potential energy at the ends where it is infinite\n",
        "    if x[i] == -a/2 or x[i]==a/2:\n",
        "        V_x[i]=1.35*ϵ[nl-1] # we can't plot ininity but extend the box to 135% of the highest plotted energy level\n",
        "plt.plot(x,V_x)\n",
        "plt.legend()\n",
        "plt.savefig(\"Infinite_Square_Well_WaveFunctions.pdf\")\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x700 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LYagRfgJ7WVt"
      },
      "source": [
        "We now also want to check that the energy levels do indeed correspond to the known levels:\n",
        "$$\n",
        "E_n = \\frac{n^2 \\pi^2 \\hbar^2}{2 m a^2}\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "NF937lC07WVt"
      },
      "source": [
        "for i in range(nl):\n",
        "    n = i+1\n",
        "    print(\"ϵ[{}] = {:9.4f},     ϵ_{} ={:9.4f},      %deviation={:>8.4f}%\".format(n,ϵ[i],n, n*n,((ϵ[i]-n*n)/n/n)))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7lkESlbs7WVu"
      },
      "source": [
        "A final test shows the accuracy of our calculation in the orthonormality of the states:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x_z7azdm5mQG"
      },
      "source": [
        "np.trapz(psi_norm[1]**2,x) # check that it works for one psi"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "25VFrevS0QKX"
      },
      "source": [
        "The code above checks the normalization of the n=2 eigenfunctions. We can check the orthonormality of a range of levels using the following lines."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i-oOP2TE7WVv"
      },
      "source": [
        "for j in range(nl):\n",
        "    for i in range(nl):\n",
        "        print(\"ψ_{}, ψ_{}, {:2.2f}\".format(i+1,j+1,np.trapz(psi_norm[i]*psi_norm[j],x)))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ELVw9a1VCSR9"
      },
      "source": [
        "Explain the results in terms of orthonormality.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fms7BS6b0iEA"
      },
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8MiJzWxOJDuE"
      },
      "source": [
        "\n",
        "## Particle in a larger box"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gRNzMq_8V0qI"
      },
      "source": [
        "Let's compare that to a particle in a box that is twice as large. Again we will calculate energies relative to the lowest level in the original box.\n",
        "\n",
        "We set up variables the same way as before. (We don't really need to redefine variables if they're not changing but it's more clear this way.)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dftiEvgeWBFx"
      },
      "source": [
        "hbar=1 # use atomic units\n",
        "m=1 # electron mass\n",
        "N = 1000\n",
        "\n",
        "a2 = 2 # the width now is twice what it was before.\n",
        "x = np.linspace(-a2/2.,a2/2.,N)\n",
        "\n",
        "Δx = x[1]-x[0] # Should be equal to 2*np.pi/(N-1). This is delta x.\n",
        "nl= 5 # the number of levels to calculate"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E45a5MG1WcTo"
      },
      "source": [
        "The operators will be the same as before.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gma4s47qWkNm"
      },
      "source": [
        "V = 0.*x # could be just zero but put x here to show that it is a function of x.\n",
        "D2 = 1./(Δx**2)*(np.diag(np.ones(N-1),-1) -2* np.diag(np.ones(N),0) + np.diag(np.ones(N-1),1)) # 2nd derivative operator\n",
        "H = -(hbar*hbar)/(2.0*m)*D2 + np.diag(V)   # Hamiltonian including derivative and potential energy.\n",
        "                                            # Again, the V is unnecessary because\n",
        "\n",
        "E2,psiT = np.linalg.eigh(H) # This computes the eigenvalues and eigenvectors of the hamiltonian matrix\n",
        "psi = np.transpose(psiT)    # We take the transpose of psiT to the wavefunction vectors can accessed as psi[n]\n",
        "                            # The eigenfunctions are returned in psiT as rows. We can access a row with the slightly\n",
        "                            # more complicated notation psiT[::,n] but renaming the transpose of the matrix makes it simpler."
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iAu8XXYpWlvl"
      },
      "source": [
        "ϵ2=[E2[i]*2/np.pi**2 for i in range(nl)]\n",
        "print(\"energy level       energy in original box       energy in 2x box       ratio\")\n",
        "for i in range(nl):\n",
        "  print(\"ϵ_{}=            {:>8.3f}                     {:>8.3f}               {:>8.3f}\".format(i+1,ϵ[i],ϵ2[i],ϵ2[i]/ϵ[i]))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DrZgWUe0Yj7L"
      },
      "source": [
        "Do these results make sense? Explain.\n",
        "\n",
        "\n",
        "Without calculating, would happen if the box were 1/2 as wide as the original box? Calculate it.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3oMEP50xAw74"
      },
      "source": [],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VsT8taoiCWr1"
      },
      "source": [
        "## Particle in a finite box"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AMFPU27ECatZ"
      },
      "source": [
        "Now we turn our attention to a problem without an easy analytical solution.\n",
        "The particle in a finite box is a similar problem but the box doesn't have infinite sides."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3n_mZ_-YCyAN"
      },
      "source": [
        "hbar=1 # Planck's constant in atomic units.\n",
        "m=1 # mass of electron\n",
        "N = 2000 # number of points to calculate\n",
        "\n",
        "a = 1.0 # width of finite box\n",
        "b=8 # total width of system\n",
        "x = np.linspace(-b/2.,b/2.,N) # x-coordinate\n",
        "\n",
        "V_out=400 #potential energy in atomic units\n",
        "\n",
        "nl=8 #number of levels to calculate\n",
        "\n",
        "lftlimit=np.searchsorted(x,[-a/2])[0]  # find the index of the left edge of the box to be used in integration later.\n",
        "                                      #searchsorted used here looks through x and finds the value closest to -a/2.\n",
        "                                      # We want to store step size, this is the reliable way:\n",
        "Δx = x[1]-x[0] # Should be equal to 2*np.pi/(N-1)"
      ],
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PXcMpoXUC1Yt"
      },
      "source": [
        "Now we set up the potential. Here we want the potential to be zero between a/2 and -a/2 and $V_0$ outside that range."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PRFCvemPC0DC"
      },
      "source": [
        "V=[]\n",
        "for i in x:\n",
        "  if i<-a/2 or i>a/2:   # if outside the box\n",
        "    V.append(V_out)     # potential is V_out\n",
        "  else:\n",
        "    V.append(0)         # inside it's 0\n",
        "#print(V)"
      ],
      "execution_count": 63,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YDB9OvVXDsmK"
      },
      "source": [
        "Now setup the operators and calculate. Everything is the same here"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kYyKHPVcxgp4"
      },
      "source": [
        "D2 = 1./(Δx**2)*(np.diag(np.ones(N-1),-1) -2* np.diag(np.ones(N),0) + np.diag(np.ones(N-1),1)) # 2nd derivative\n",
        "H = -(hbar*hbar)/(2.0*m)*D2 + np.diag(V) # Hamiltonian\n",
        "\n",
        "Ef,psiT = np.linalg.eigh(H) # This computes the eigen values and eigenvectors\n",
        "psi = np.transpose(psiT)  # We take the transpose of psiT to the wavefunction vectors can accessed as psi[n]\n",
        "\n",
        "Ef=Ef/(hbar**2 * np.pi**2/2/m/a**2) # scale energy relative to standard particle in an infinite box. hbar, m, and a are set to 1\n",
        "                                  # so all energies are in units of hbar**2/(m*a**2)\n",
        "V=[V/(hbar**2 * np.pi**2/2/m/a**2) for V in V] # same for potential energy."
      ],
      "execution_count": 64,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 435
        },
        "id": "wPgumM6UEqdg",
        "outputId": "adbb14cc-419e-44a8-e0e8-fc51b59ee9b3"
      },
      "source": [
        "norm=[np.sqrt(1/np.trapz(psi[i]**2,x)) for i in range(nl)]  # calcluate normalization coefficient (sqrt of 1/integral of psi squared)\n",
        "                                                            # Should be same but no cost to calculate for each level.\n",
        "                                                            # trapz is numpy's (trapezoidal) integration function. input function and the variable\n",
        "for i in range(0,nl): # start with i=1 and go to i=\n",
        "  if psi[i][lftlimit] < 0:   # Flip the wavefunctions if it is negative at large x, so plots are more consistent.\n",
        "      psi_norm[i]=-psi[i]*norm[i]\n",
        "  else:\n",
        "      psi_norm[i]=psi[i]*norm[i-1]\n",
        "\n",
        "plt.plot(x,psi_norm[2]+Ef[2])# plot third wavefunction to make sure it looks right.\n",
        "plt.ylim(-1,12) # change or comment out with a # if you want to look at other eigenfunctions\n",
        "plt.xlim(-2,2)\n",
        "plt.plot(x,V)\n",
        "plt.show()\n"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mB4oXMenBn8p"
      },
      "source": [
        "Check to make sure the wavefunctions are normalized."
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "1MhPC5wrVxA3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S-TRnFLfBtXQ"
      },
      "source": [
        "As before, let's plot several wavefunctions on the same graph offset by their energies. It should be emphasized that all particles are travelling only on the $x$-axis. Offsetting along the $y$-axis only gets them out of each other's way and shows where the energy levels are."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 699
        },
        "id": "sfS2AasT02Uo",
        "outputId": "bf7b12c9-bac6-49c0-c3bf-f23abaa7e36f"
      },
      "source": [
        "#plot several wavefunctions on same graph with potential. Each one placed at its energy level.\n",
        "plt.figure(figsize=(5,8))\n",
        "for i in range(0,nl):\n",
        "  plt.plot(x,psi_norm[i]+Ef[i],label=\"$E_{}$={:>8.3f}\".format(i+1,Ef[i]))\n",
        "plt.title(\"Eigenfunctions of the Finite Square Well\")\n",
        "\n",
        "plt.plot(x,V)\n",
        "plt.xlim(-a*.8,a*.8)\n",
        "#plt.legend()\n",
        "#plt.savefig(\"Finite_Square_Well_WaveFunctions.pdf\")\n",
        "plt.show()\n"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zKecH3dECDB4"
      },
      "source": [
        "Do the same thing for the square of the wavefunction."
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "c9cHyf4tX1yq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wtH9wIkC29WL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 699
        },
        "outputId": "0a22e64a-7dc4-45cb-ad3f-aa8193b1cc85"
      },
      "source": [
        "#plot square of wavefunction\n",
        "plt.figure(figsize=(5,8))\n",
        "for i in range(nl):\n",
        "    plt.plot(x,psi_norm[i]**2+Ef[i],label=\"$E_{}$={:>8.3f}\".format(i+1,Ef[i])) # make a plot for each level and label it\n",
        "plt.title(\"Finite Well Wavefunctions Squared\")\n",
        "plt.plot(x,V)\n",
        "plt.legend()\n",
        "plt.xlim(-.8*a,.8*a)\n",
        "#plt.savefig(\"Finite_Square_Well_WaveFunctions_Squared.pdf\")\n",
        "plt.show()"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1NDnuO6JSu-y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "50d9f31e-f203-431f-da34-bcce1db84dd8"
      },
      "source": [
        "ϵ2=[Ef[i]*2/np.pi**2 for i in range(nl)]\n",
        "print(\"energy level       energy in infinite box       energy in finite box       ratio\")\n",
        "for i in range(nl):\n",
        "  print(\"ϵ_{}=            {:>8.3f}                     {:>8.3f}               {:>8.3f}\".format(i+1,ϵ[i],Ef[i],Ef[i]/ϵ[i]))"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "energy level       energy in infinite box       energy in finite box       ratio\n",
            "ϵ_1=               0.996                        0.871                  0.875\n",
            "ϵ_2=               3.984                        3.482                  0.874\n",
            "ϵ_3=               8.964                        7.823                  0.873\n",
            "ϵ_4=              15.936                       13.882                  0.871\n",
            "ϵ_5=              24.900                       21.631                  0.869\n",
            "ϵ_6=              35.855                       31.034                  0.866\n",
            "ϵ_7=              48.802                       42.025                  0.861\n",
            "ϵ_8=              63.741                       54.483                  0.855\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kYWe_zMO9bTt"
      },
      "source": [
        "We can see that $\\psi$ does not go to zero at the end of the box the way that it did in the infinite box. This is especially noticeable for the higher levels. We can integrate $\\psi$ from a/2 to b (i.e. the region on the right outside the box) and multiply by 2 to get the total area on both sides. The $trapz$ integration function for numerical trapezoidal integration takes for arguments $y$ and $x$. In our case we'll take $psi$ for the $i$th level from the right boundary to the end (psi[i][rgtlimit:]) and square it, normalize it, and integrate."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jE5lvUuLgk4a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c751407c-cd92-429c-d5f7-19de499b2abb"
      },
      "source": [
        "outob=[np.trapz((psi_norm[i][:lftlimit])**2,x[:lftlimit])*2 for i in range(0,nl)] #integrate from the left edge of the box to -'infinity' and multipy by 2 to account for both sides\n",
        "for i in range(0,nl):\n",
        "      print(\"n={}, E[{}] = {:9.4f},         Probability to be outside box={:7.3f},              Percent outside box={:5.1f}%\".format(i+1,i+1,E[i],outob[i],outob[i]*100))"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "n=1, E[1] =    4.9151,         Probability to be outside box=  0.001,              Percent outside box=  0.1%\n",
            "n=2, E[2] =   19.6603,         Probability to be outside box=  0.003,              Percent outside box=  0.3%\n",
            "n=3, E[3] =   44.2356,         Probability to be outside box=  0.006,              Percent outside box=  0.6%\n",
            "n=4, E[4] =   78.6406,         Probability to be outside box=  0.011,              Percent outside box=  1.1%\n",
            "n=5, E[5] =  122.8750,         Probability to be outside box=  0.019,              Percent outside box=  1.9%\n",
            "n=6, E[6] =  176.9385,         Probability to be outside box=  0.029,              Percent outside box=  2.9%\n",
            "n=7, E[7] =  240.8303,         Probability to be outside box=  0.044,              Percent outside box=  4.4%\n",
            "n=8, E[8] =  314.5500,         Probability to be outside box=  0.069,              Percent outside box=  6.9%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_oXianwGlFY-"
      },
      "source": [
        "## Particle in an asymmetric box"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eQxEhbEiatvo"
      },
      "source": [
        "hbar=1 # Planck's constant in atomic units.\n",
        "m=1 # mass of electron\n",
        "N = 2000 # number of points to calculate\n",
        "\n",
        "a = 1.0 # width of finite box\n",
        "bar=5.0 # with of barrier\n",
        "b=10 # total width of system\n",
        "\n",
        "V_out=400 #potential energy in atomic units\n",
        "nl=8 #number of levels to calculate\n",
        "x = np.linspace(-a/2.,b/2.,N) # x-coordinate\n",
        "rgtlimit=np.searchsorted(x,[a/2])[0] # find the index of the right edge of the box to be used in integration later.\n",
        "                                    #searchsorted used here looks through x and finds the value closest to a/2.\n",
        "\n",
        "Δx = x[1]-x[0]                      #step size\n",
        "\n",
        "V=[]                                #potential -\n",
        "for i in x:\n",
        "  if i>a/2:\n",
        "    V.append(V_out)                 # potential on the right\n",
        "  else:\n",
        "    V.append(0)                     # potential in the box\n",
        "                                    # potential on the left is infinite which\n",
        "#print(V)\n",
        "\n",
        "D2 = 1./(Δx**2)*(np.diag(np.ones(N-1),-1) -2* np.diag(np.ones(N),0) + np.diag(np.ones(N-1),1))\n",
        "H = -(hbar*hbar)/(2.0*m)*D2 + np.diag(V)\n",
        "\n",
        "Ea,psiT = np.linalg.eigh(H) # This computes the eigen values and eigenvectors\n",
        "psi = np.transpose(psiT)  # We take the transpose of psiT to the wavefunction vectors can accessed as psi[n]\n",
        "\n",
        "norm=[np.sqrt(1/np.trapz(psi[i]**2,x)) for i in range(nl)] #calcluate normalization coefficient. Should be same but no cost to calculate for each level.\n",
        "Ea=Ea/np.pi**2*2 # scale energy relative to standard particle in an infinite box\n",
        "V=[V/np.pi**2*2 for V in V] # same for potential energy.\n",
        "\n",
        "psi_norm=[psi[i]*norm[i] for i in range(nl)] # normalize"
      ],
      "execution_count": 87,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 431
        },
        "id": "0CeTzOZCbgA2",
        "outputId": "370144bc-588e-4380-da7f-37abbb142a05"
      },
      "source": [
        "#plot square of wavefunction\n",
        "V_x =V # potential energy is just zeros. We don't need it for calculating but we do for plotting\n",
        "for i in range(N): # but adjust potential energy at the ends where it is infinite\n",
        "    if x[i] == -a/2:\n",
        "        V_x[i]=1.35*Ea[nl-1] # we can't plot ininity but extend the box to 135% of the highest plotted energy level\n",
        "plt.figure(figsize=(20,7))\n",
        "for i in range(nl):\n",
        "    plt.plot(x,psi_norm[i]**2*fact**2+Ea[i],label=\"$E_{}$={:>8.3f}\".format(i+1,Ea[i]))\n",
        "plt.title(\"Finite Well Wavefunctions Squared\")\n",
        "plt.plot(x,V_x,color='black')\n",
        "plt.xlim(-a,a+bar)\n",
        "plt.legend()\n",
        "#plt.savefig(\"Finite_Square_Well_WaveFunctions_Squared.pdf\")\n",
        "plt.show()"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x700 with 1 Axes>"
            ],
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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ϵ2=[Ea[i]*2/np.pi**2 for i in range(nl)]\n",
        "print(\"energy level       energy in infinite box       energy in finite box       ratio\")\n",
        "for i in range(nl):\n",
        "  print(\"ϵ_{}=            {:>8.3f}                     {:>8.3f}               {:>8.3f}\".format(i+1,ϵ[i],Ea[i],Ea[i]/ϵ[i]))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "x3sQQi0mblgr",
        "outputId": "ebd30df6-af66-4a0a-8382-46b672a2364f"
      },
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "energy level       energy in infinite box       energy in finite box       ratio\n",
            "ϵ_1=               0.996                        0.928                  0.931\n",
            "ϵ_2=               3.984                        3.709                  0.931\n",
            "ϵ_3=               8.964                        8.338                  0.930\n",
            "ϵ_4=              15.936                       14.808                  0.929\n",
            "ϵ_5=              24.900                       23.102                  0.928\n",
            "ϵ_6=              35.855                       33.197                  0.926\n",
            "ϵ_7=              48.802                       45.049                  0.923\n",
            "ϵ_8=              63.741                       58.569                  0.919\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "outob=[np.trapz((psi_norm[i][rgtlimit:])**2,x[rgtlimit:]) for i in range(0,nl)] #integrate from the right edge of the box to 'infinity'\n",
        "for i in range(0,nl):\n",
        "      print(\"n={}, E[{}] = {:9.4f},         Probability to be outside box={:7.3f},              Percent outside box={:5.1f}%\".format(i+1,i+1,E[i],outob[i],outob[i]*100))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BGJH-xUYbDeH",
        "outputId": "c908412f-8154-48cf-dbe6-2576a0b41100"
      },
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "n=1, E[1] =    4.9151,         Probability to be outside box=  0.000,              Percent outside box=  0.0%\n",
            "n=2, E[2] =   19.6603,         Probability to be outside box=  0.001,              Percent outside box=  0.1%\n",
            "n=3, E[3] =   44.2356,         Probability to be outside box=  0.003,              Percent outside box=  0.3%\n",
            "n=4, E[4] =   78.6406,         Probability to be outside box=  0.006,              Percent outside box=  0.6%\n",
            "n=5, E[5] =  122.8750,         Probability to be outside box=  0.011,              Percent outside box=  1.1%\n",
            "n=6, E[6] =  176.9385,         Probability to be outside box=  0.017,              Percent outside box=  1.7%\n",
            "n=7, E[7] =  240.8303,         Probability to be outside box=  0.027,              Percent outside box=  2.7%\n",
            "n=8, E[8] =  314.5500,         Probability to be outside box=  0.043,              Percent outside box=  4.3%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Double square well"
      ],
      "metadata": {
        "id": "_pkbNy1qa37A"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wKoXkeHuy7JM"
      },
      "source": [
        "hbar=1 # Planck's constant in atomic units.\n",
        "m=1 # mass of electron\n",
        "N = 2047 # number of points to calculate\n",
        "a = 1.0 # width of finite box\n",
        "bar=12 # with of barrier\n",
        "b=50 # total width of system\n",
        "V0=200 #potential energy in atomic units\n",
        "Vb=200 #height of barrier\n",
        "nl=20 #number of levels to calculate\n",
        "x = np.linspace(-b/2.,b/2.,N) # x-coordinate\n",
        "rgtlimit=np.searchsorted(x,[a/2])[0] # find the index of the right edge of the box to be used in integration later.\n",
        "#searchsorted used here looks through x and finds the value closest to a/2.\n",
        "# We want to store step size, this is the reliable way:\n",
        "h = x[1]-x[0] # Should be equal to 2*np.pi/(N-1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5VF0mY8YzK6w"
      },
      "source": [
        "V=[]\n",
        "for i in x:\n",
        "  if i>-bar/2 and i<bar/2:\n",
        "    V.append(Vb)\n",
        "  elif (i>(-bar/2-a) and i<-bar/2) or (i<(bar/2+a) and i>bar/2):\n",
        "    V.append(0)\n",
        "  else:\n",
        "    V.append(V0)\n",
        "#print(V)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y2p-j4nl0eIo"
      },
      "source": [
        "D2 = 1./(h*h)*(np.diag(np.ones(N-1),-1) -2* np.diag(np.ones(N),0) + np.diag(np.ones(N-1),1))\n",
        "H = -(hbar*hbar)/(2.0*m)*D2 + np.diag(V)\n",
        "Ed,psiT = np.linalg.eigh(H) # This computes the eigenvalues and eigenvectors\n",
        "psi = np.transpose(psiT)  # We take the transpose of psiT to the wavefunction vectors can accessed as psi[n]\n",
        "norm=[np.sqrt(1/np.trapz(psi[i]**2,x)) for i in range(nl)] #calcluate normalization coefficient. Should be same but no cost to calculate for each level.\n",
        "Ed=Ed/np.pi**2*2 # scale energy relative to standard particle in an infinite box\n",
        "V=[V/np.pi**2*2 for V in V] # same for potential energy.\n",
        "psi_norm=[psi[i]*norm[i] for i in range(nl)] # normalize\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 503
        },
        "id": "Es_tvBD40xwL",
        "outputId": "1044f187-1edc-402d-bc43-40355a0297b4"
      },
      "source": [
        "#plot several wavefunctions on same graph with potential. Each one placed at its energy level.\n",
        "fact=1 #scale factor for nice plotting. 1 does nothing but if the plots need to be scaled up or down, change it.\n",
        "plt.figure(figsize=(20,7))\n",
        "for i in range(nl):\n",
        "    if psi[i][50] < 0:   # Flip the wavefunctions if it is negative at small x, so plots are more consistent.\n",
        "        plt.plot(x,-psi_norm[i]*fact+Ed[i],label=\"$E_{}$={:>8.3f}\".format(i+1,Ed[i]))\n",
        "    else:\n",
        "        plt.plot(x,psi_norm[i]*fact+Ed[i],label=\"$E_{}$={:>8.3f}\".format(i+1,Ed[i]))\n",
        "    plt.title(\"Solutions to the Finite Double Square Well\")\n",
        "\n",
        "plt.plot(x,V)\n",
        "plt.xlim(-(a+bar),(a+bar))\n",
        "#plt.legend()\n",
        "#plt.savefig(\"Finite_Square_Well_WaveFunctions.pdf\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x700 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 503
        },
        "id": "PKvb4bz64r1b",
        "outputId": "6914d44c-0b17-467f-87d7-f692111742b0"
      },
      "source": [
        "#plot square of wavefunction\n",
        "plt.figure(figsize=(20,7))\n",
        "for i in range(nl):\n",
        "    plt.plot(x,psi_norm[i]**2*fact**2+Ed[i],label=\"$E_{}$={:>8.3f}\".format(i+1,Ed[i]))\n",
        "plt.title(\"Finite Double Well Wavefunctions Squared\")\n",
        "plt.plot(x,V)\n",
        "plt.xlim(-a-bar,a+bar)\n",
        "plt.legend()\n",
        "#plt.savefig(\"Finite_Square_Well_WaveFunctions_Squared.pdf\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x700 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 503
        },
        "id": "q2bbo7Yt7zCR",
        "outputId": "18da4a4b-b947-4cad-991e-5975560e25b1"
      },
      "source": [
        "#@title Double Well Probability\n",
        "l = 0 #@param {type:\"slider\", min:0, max:15, step:1}\n",
        "#plot square of wavefunction\n",
        "plt.figure(figsize=(20,7))\n",
        "plt.plot(x,psi_norm[l]**2*fact**2+Ed[l],label=\"$E_{}$={:>8.3f}\".format(l+1,Ed[l]))\n",
        "plt.title(\"Finite Well Wavefunctions Squared\")\n",
        "plt.plot(x,V)\n",
        "plt.legend()\n",
        "#plt.savefig(\"Finite_Square_Well_WaveFunctions_Squared.pdf\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x700 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Appendices\n"
      ],
      "metadata": {
        "id": "DkcuHT4C-bpw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#####Matrix Multiplication\n",
        "If you have not taken linear algebra it will be useful to see the mechanics of multplication of a small matrix with a vector. We will use a 3x3 matrix, $O$ (for $operator$) and a 3x1 vector, $f$ (for $function$) as examples.\n",
        "$$O=\\begin{bmatrix}1&0&3\\\\0&5&4\\\\2&6&0\\end{bmatrix}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,f=\\begin{bmatrix} 1\\\\2\\\\3\\end{bmatrix}$$\n",
        "Multiplication of the vector by the matrix leads to a 3x1 vector. The first element comes from the sum of the top leftmost element multiplied by the first element of the vector, the top-center element multiplied of the matrix by the second element of the vector and the top rightmost element of the matrix multiplied by the last element of the vector. In other words the first element of the product is the sum of the elemnts on the first row of the matrix multiplied by the first (only) column of the vector.\n",
        "\n",
        "$$Of=\\begin{bmatrix}1&0&3\\\\0&5&4\\\\2&6&0\\end{bmatrix}\\begin{bmatrix} 1\\\\2\\\\3\\end{bmatrix}=\\begin{bmatrix}1\\cdot1+0\\cdot2+3\\cdot3\\\\0\\cdot1+5\\cdot2+4\\cdot3\\\\2\\cdot1+6\\cdot2+0\\cdot3\\end{bmatrix}=\\begin{bmatrix}10\\\\22\\\\14\\end{bmatrix}$$\n",
        "In this case our vector is not an eigenvector of the matrix because it doesn't emerge from the multiplication as a constant times the original vector.\n",
        "Multiplying two matrices is similar but we won't worry about that now.\n",
        "\n",
        "We can do this matrix multiplication in python too."
      ],
      "metadata": {
        "id": "xsj8ZRIiPpNr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np # load package needed for dealing with matrices and numerical calculations."
      ],
      "metadata": {
        "id": "uPVV4-Wy133Q"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xncbmuz0zuCL"
      },
      "source": [
        "O=np.array([[1,0,3],[0,5,4],[2,6,0]])\n",
        "#print(O) # if you want to see O, remove the first # and run the cell\n",
        "f=np.array([[1],[2],[3]])\n",
        "O.dot(f) # np.dot(O,f) works too"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FQR8q5M50bXm"
      },
      "source": [
        "Try multiplying $$\\begin{bmatrix} 1&-1&0\\\\-1&1&-1\\\\ 0&-1&1\\end{bmatrix}$$ by $$\\begin{bmatrix}2\\\\3\\\\1\\end{bmatrix}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e42sQYpk4SwZ"
      },
      "source": [],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## np.diag and np.ones\n",
        "To make a derivative matrix with ones and minus ones on some diagonals, it is convenient to use numpy's ```diag``` function. ```np.diag([1,2,3])``` makes a matrix with 1, 2, and 3 along the diagonal and zeros elsewhere. Likewise, we can insert elements along a *subdiagonal* or *superdiagonal* (the diagonal below or above the true diagonal of a square matrix) using ```np.diag([1,2,3],1]```\n",
        "\n"
      ],
      "metadata": {
        "id": "5W2m_ana1yrl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.diag([1,2,3])"
      ],
      "metadata": {
        "id": "1XqFVh0HHBFK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.diag([1,2,3],-1)"
      ],
      "metadata": {
        "id": "SgY7f02SG6m7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We have seen that a matrix with -1 on the diagonal just above the diagonal will make a derivative operator.  We can do this using ```np.diag([-1,-1,-1,-1,-1,-1])``` which works fine if we know just how big our matrix is going to be. But if we want to adjust things, we'll have to remember to adjust the number of 1's in our diagonal matrix.\n",
        "\n",
        "We can make use of ```np.ones``` to generate a list of ones that is adjustable. So ```np.diag(-np.ones(5))``` will give a 5x5 matrix with -1 on the diagonal and ```np.diag(np.ones(4),1)``` will give a 5x5 matrix with +1 on the superdiagonal. These can be added to give the deriviative matrix we want. Substituting a variable such as $N$ and $N-1$ instead of 5 and 4 will make it so that just changing the value of $N$ will adjust the size of the derivative matrix so we can handle whatever size f(x) vector we want.\n",
        "\n",
        "[back to derivative calculation](#scrollTo=MsgIOf7cEFkv&line=1&uniqifier=1)"
      ],
      "metadata": {
        "id": "Qb0LY9a0HKhd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##forward and backward derivatives\n",
        "When we say forward derivative, we're talking about the technique of taking the derivative of a discretized function by taking finding the slope using the difference between $f(x+Δx)$ and $f(x)$ wheras a backward deriviate would use $f(x)$ and $f(x-Δx)$. There's no reason to prefer one over the other. The main effect of the choice will be whether to ignore the first or the last element of the result since there's no $f(x+Δx)$ at the last element and no $f(x-Δx)$ at the first element. We get to choose.\n",
        "\n",
        "When calculating the second derivative, we could do each derivative forward which would result in a derivative that would look like $$\n",
        "\\frac{d^2}{dx^2}f(x) = \\lim_{\\Delta x \\rightarrow 0} \\frac{f'(x+\\Delta x)-f'(x)}{\\Delta x} =  \\lim_{\\Delta x \\rightarrow 0} \\frac{f(x+\\Delta x+\\Delta x) - f(x+\\Delta x) - (f(x+\\Delta x) - f(x))}{\\Delta x^2} \\\\\n",
        "\\frac{d^2}{dx^2}f(x) = \\lim_{\\Delta x \\rightarrow 0} \\frac{f(x+2\\Delta x) - 2f(x+\\Delta x) + f(x))}{\\Delta x^2} \\approx \\frac{f(x+2h) - 2f(x+h) + f(x))}{h^2}\n",
        "$$\n",
        "This second derivative is really leaning forward enough that we should consider it a derivative around $x+Δx$ rather than around $x$. Therefore it makes sense to take the second derivative in the opposite direction as we took the first. Since we chose to do a forward first derivative, we choose a backward second derivative. This means that both the first element and last elements of our resulting 2nd derivative vector are meaningless.\n",
        "\n",
        "[Back to the second order differential section](#scrollTo=eEvfX6Yb7WRX&line=6&uniqifier=1)"
      ],
      "metadata": {
        "id": "WtiOKVHUEPlB"
      }
    }
  ]
}