Numerical solutions of the time-dependent Schrodinger equation in two dimensions

Abstract

The generalized Crank-Nicolson method is employed to obtain numerical solutions of the two-dimensional time-dependent Schrodinger equation. An adapted alternating-direction implicit method is used, along with a high-order finite difference scheme in space. Extra care has to be taken for the needed precision of the time development. The method permits a systematic study of the accuracy and efficiency in terms of powers of the spatial and temporal step sizes. To illustrate its utility the method is applied to several two-dimensional systems.

arXiv comment11 pages, 9 figures

References in corpus (4)

• Controlled double-slit electron diffraction
• Accurate numerical solutions of the time-dependent Schrödinger equation
• Efficient and accurate methods for solving the time-dependent spin-1 Gross-Pitaevskii equation
• Numerical solutions of the Schrodinger equation with source terms or time-dependent potentials

Cited by in corpus (2)

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