Asymptotic behavior of numerical solutions of the Schrodinger equation

Abstract

Many problems of numerically solving the Schrodinger equation require that we choose asymptotic
distances many times greater than the characteristic size of the region of interaction. The problems of
resonance diffraction for composite particles or the problem of nucleon scattering by nonspherical atomic
nuclei are examples of the need to use a large spatial domain for calculations. If the solution to onedimensional
equations can be immediately chosen in a form that preserves unitarity, the invariance of
probability (in the form of, e.g., fulfilling an optical theorem) is a real problem for two-dimensional
equations. An addition that does not exceed the discretization error and ensures a high degree of unitarity
is proposed as a result of studying the properties of a discrete two-dimensional equation.
The problem for scattering of rigid molecules by the disks was successfully solved using an improved
sampling scheme that provides the correct asymptotic behavior. Corresponding diffraction scattering
curves are of a pronounced resonance nature.