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removed some stuff from notebook messing with other cells
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edinvay authored and bjorgve committed Nov 24, 2023
1 parent e754f13 commit 2c52b30
Showing 1 changed file with 13 additions and 6 deletions.
19 changes: 13 additions & 6 deletions docs/notebooks/harmonic_oscillator_evolution.ipynb
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"id": "f4f5c5cf",
"metadata": {},
"source": [
"**Constructor Parameters**\n",
"- `expA`: stands for operator $\\exp \\left( \\frac t2 A \\right) = \\exp \\left( i \\frac t2 \\partial_x^2 \\right)$\n",
"- `expB`: stands for operator $\\exp \\left( \\frac t6 B \\right) = \\exp \\left( -i \\frac t6 V \\right)$\n",
"- `exp_tildeB`: stands for operator $\\exp \\left( \\frac {2t}3 \\widetilde B \\right) = \\exp \\left( -i \\frac {2t}3 \\widetilde V \\right)$ with\n",
"`expA`: stands for operator $\\exp \\left( \\frac t2 A \\right) = \\exp \\left( i \\frac t2 \\partial_x^2 \\right)$\n",
"\n",
"\n",
"`expB`: stands for operator $\\exp \\left( \\frac t6 B \\right) = \\exp \\left( -i \\frac t6 V \\right)$\n",
"\n",
"\n",
"`exp_tildeB`: stands for operator\n",
"$\n",
"\\widetilde V\n",
" \\exp \\left( \\frac {2t}3 \\widetilde B \\right) = \\exp \\left( -i \\frac {2t}3 \\widetilde V \\right)\n",
"$\n",
"with\n",
"$\n",
" \\widetilde V\n",
" =\n",
" V\n",
" -\n",
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" - \\frac {(x - x_0)^2}{4 \\sigma^2}\n",
" \\right)\n",
"\\end{equation*}\n",
"with $x_0 = 0.3$, $p = 0$ and $\\sigma = 0.04$.\n",
"with $x_0 = 0.3$ and $\\sigma = 0.04$.\n",
"All the parameters are chosen in a way that the solution\n",
"stays localized mainly on the space interval $[0, 1]$."
]
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