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Open Quantum Systems Decoherence Quantum Simulation

Numerical solutions of the Schrodinger equation with source terms or time-dependent potentials

arXiv
Authors: W. van Dijk, F. M. Toyama

Year

2014

Paper ID

46076

Status

Preprint

Abstract Read

~2 min

Abstract Words

83

Citations

N/A

Abstract

We develop an approach to solving numerically the time-dependent Schrodinger equation when it includes source terms and time-dependent potentials. The approach is based on the generalized Crank-Nicolson method supplemented with an Euler-MacLaurin expansion for the time-integrated nonhomogeneous term. By comparing the numerical results with exact solutions of analytically solvable models, we find that the method leads to precision comparable to that of the generalized Crank-Nicolson method applied to homogeneous equations. Furthermore, the systematic increase in precision generally permits making estimates of the error.

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  • We develop an approach to solving numerically the time-dependent Schrodinger equation when it includes source terms and time-dependent potentials.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1412.1802 [2] arXiv https://arxiv.org/abs/1412.1802 [3] Publisher https://arxiv.org/abs/1412.1802

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