'lin var documented'

ch06/demo_lin_var.ipynb

@@ -168,7 +168,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 42,
    "metadata": {},
    "outputs": [
     {
@@ -185,20 +185,20 @@
     "num_basis_functions = 2\n",
     "\n",
     "# Compute the overlap matrix and Hamiltonian matrix\n",
-    "overlap_matrix = np.zeros((num_basis_functions, num_basis_functions))\n",
-    "hamiltonian_matrix = np.zeros((num_basis_functions, num_basis_functions))\n",
+    "S = np.zeros((num_basis_functions, num_basis_functions))\n",
+    "H = np.zeros((num_basis_functions, num_basis_functions))\n",
     "\n",
     "for i in range(num_basis_functions):\n",
     "    for j in range(num_basis_functions):\n",
     "\n",
     "        fi, fj = basis_functions(x, i), basis_functions(x, j)\n",
     "\n",
-    "        overlap_matrix[i, j]     = np.trapz(fi * fj, x=x)\n",
+    "        S[i, j]     = np.trapz(fi * fj, x=x)\n",
     "\n",
-    "        hamiltonian_matrix[i, j] = np.trapz(fi * KE(fj, dx) + fi * PE(fj, x), x=x)\n",
+    "        H[i, j] = np.trapz(fi * KE(fj, dx) + fi * PE(fj, x), x=x)\n",
     "\n",
     "# Diagonalize the matrices to find eigenvalues and eigenvectors\n",
-    "eigenvalues, eigenvectors = eigh(hamiltonian_matrix, overlap_matrix)\n",
+    "eigenvalues, eigenvectors = eigh(H, S)\n",
     "\n",
     "# Find the ground-state energy (lowest eigenvalue) and corresponding eigenfunction\n",
     "ground_state_energy = eigenvalues[0]\n",
@@ -212,7 +212,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### visualize Eigenfunctions and eigenvalues"
+    "### Visualize Eigenfunctions and eigenvalues"
    ]
   },
   {
@@ -266,13 +266,6 @@
     "ax2.set_xlim(-3, 4)\n",
     "ax2.set_title('Energy levels')"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {