Asymptotic Behavior of Solutions in Finite-Difference Schemes

Abstract

In many problems of numerically solving the Schrödinger equation, it is necessary to choose asymptotic distances that are many times greater than the characteristic size of the region of interaction. If the solutions to one-dimensional equations can be immediately chosen in a form that preserves unitarity, the preservation of probability (in, e.g., the form of optical theorem implementation) is then a real problem for two-dimensional equations. As result of studying the properties of a discretized two-dimensional equation, an additional term is found that does not exceed the sampling error and ensures a high degree of unitarity preservation.