Numerical solutions of the time-dependent Schrödinger equation in two dimensions.
basic_science · Level V
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- Record sourced from PubMed, PMID 28298000.
- Also identified by DOI 10.1103/PhysRevE.95.023310.
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Abstract
The generalized Crank-Nicolson method is employed to obtain numerical solutions of the two-dimensional time-dependent Schrödinger 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.