Non-relativistic Fermi particle in one-dimensional pseudoscalar ${\delta}$-function potential

TL;DR

This paper investigates the behavior of a non-relativistic Fermi particle in a one-dimensional pseudoscalar delta-function potential, revealing how its rest energy influences confinement, bound states, and scattering properties.

Contribution

It introduces a detailed analysis of how non-zero rest energy affects bound states and scattering in a pseudoscalar delta potential, extending prior models to include rest energy effects.

Findings

Particles can be confined for both signs of coupling constant.

Binding energies depend on the particle's rest energy.

Reflection and transmission coefficients are explicitly determined.

Abstract

It is shown that a non-relativistic Fermi particle with a non-zero rest energy moving in a pseudoscalar ${\delta}$-function potential in one dimension can be confined for both signs of the coupling constant. The binding energies depend on the value of the particle's rest energy, and in the limit of vanishing rest energy only one of the bound states survives. The coefficients of reflection and transmission are determined, and the conditions for complete reflection and transmission are discussed.