Lattice Discretization in Quantum Scattering

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.

9 pages

Cited by in corpus (10)

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• Dimensional versus cut-off renormalization and the nucleon-nucleon interaction
• Singularity-free treatment of delta-function point scatterers in two dimensions and its conceptual implications
• Scattering by a collection of $\delta$-function point and parallel line defects in two dimensions
• Renormalization of multi-delta-function point scatterers in two and three dimensions, the coincidence-limit problem, and its resolution
• Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium