20 lines
1.1 KiB
TeX
20 lines
1.1 KiB
TeX
\documentclass[../schrodinger_simulation.tex]{subfiles}
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\begin{document}
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\begin{abstract}
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We have simulated the two-dimensional time-dependent Schrödinger equation, to study
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variations of the double-slit experiment. To derive a discretized equation
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we applied the Crank-Nicolson scheme in 2+1 dimensions. In addition, we have used
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Dirichlet boundary conditions to express the equation in matrix form, and solve
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it using the sparse matrix solver \verb|superlu|. Our implementation, and choice
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of solver method, resulted in a deviation from conserved total probability on the
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scale $10^{-14}$, for both the single and double slit setup. To illustrate the time
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evolution of the probability function, we created colormap plots for time steps
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$t=\{0, 0.001, 0.002\}$. We also included separate plots for each time step of
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Re$(u_{\ivec, \jvec})$ and Im$(u_{\ivec, \jvec})$. In addition, we determined the
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normalized particle detection probability $p(y \ | \ x=0.8, t=0.002)$, for single-,
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double- and triple-slit.
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\end{abstract}
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\end{document}
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% $| \sum_{\ivec, \jvec} p_{\ivec, \jvec}^{n} - 1 | \approx $ |