Lattice Discretization in Quantum Scattering

TL;DR

This paper demonstrates how lattice discretization can effectively solve nonrelativistic quantum scattering problems, especially handling ultraviolet divergences with singular potentials, exemplified by the Dirac delta function potential.

Contribution

It introduces lattice discretization as a practical numerical method for quantum scattering, addressing divergence issues in singular potentials.

Findings

Successfully applied to Dirac delta potential

Handles ultraviolet divergences effectively

Potentially useful for general scattering problems

Abstract

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin in two and three space dimensions. This shows that lattice discretization technique could be a useful tool for the numerical solution of scattering problems in general. The approach is illustrated in the case of the Dirac delta function potential.