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HOTFIX: Removed \label usages from markdown files, unrecognized contr…
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…ol sequence by KaTeX
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gsgrattan committed Jan 28, 2025
1 parent 90915b3 commit 078d656
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions notebooks/RuClExample.ipynb
Original file line number Diff line number Diff line change
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" \\Omega(s) = \\sum_{k=0}^{\\infty} \\Omega_k(s)\n",
"\\end{equation}\n",
"with the terms of the sum given by the recursive formula,\n",
"\\begin{equation}\\label{eq:recursive_magnus}\n",
"\\begin{equation}\n",
"\\begin{split}\n",
" \\Omega_k(s) &= \\sum_{j = 1}^{k-1} \\frac{B_j}{j!} \\int_{0}^{s} S_k^{(j)}(s_1) ds_1, k > 1 \\\\\n",
" \\Omega_1(s) &= \\int_{0}^{s} A(s_1) ds_1\n",
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" \\begin{split}\n",
" S_{k}^{(1)}(s) &= \\left[ \\Omega_{k-1}(s), A(s)\\right] \\\\\n",
" S_{k}^{(j)}(s) &= \\sum_{l=1}^{n-j} \\left[ \\Omega_{l}(s), S_{k-l}^{(j-1)(s)} \\right], j > 1.\n",
" \\end{split} \\label{eq:magnus-generic-terms}\n",
" \\end{split} \n",
"\\end{equation}\n",
"The first three terms in the expansion of $\\Omega(t)$ can be written explicitly as\n",
"\\begin{equation}\\label{eq:explicit_magnus}\n",
"\\begin{equation}\n",
" \\begin{split}\n",
" \\Omega_1(s) &= \\int_{0}^{s} ds_1 \\bigl(A(s_1) \\bigr), \\\\ \n",
" %\n",
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"for $T\\geq t\\geq s$, the unitary matrix solution \n",
"of the time-dependent Schrodinger equation, \n",
"\\begin{equation}\n",
"i\\frac{d}{dt}\\hat{U}\\left(t;s\\right)=\\hat{H}\\left(t\\right)\\hat{U}\\left(t;s\\right),\\label{eq:app_time_dep_schro} \n",
"i\\frac{d}{dt}\\hat{U}\\left(t;s\\right)=\\hat{H}\\left(t\\right)\\hat{U}\\left(t;s\\right),\n",
"\\end{equation}\n",
"\n",
"with $\\hat{U}\\left(s;s\\right)=I$. We assume that the Hamiltonian has the form $H\\left(t\\right)=a\\left(t\\right)\\hat{A}+b\\left(t\\right)\\hat{B}$, where the operators $\\hat{A}$ and $\\hat{B}$ do not commute and that the functions $a\\left(t\\right)$ and $b\\left(t\\right)$\n",
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