Rest energy effects for non-relativistic Fermi fields in external potentials

TL;DR

This paper investigates how the rest energy of non-relativistic Fermi fields influences bound state spectra in external potentials, using the generalized Levy-Leblond equation to analyze conditions where rest energy effects are significant.

Contribution

It identifies conditions under which the rest energy can be removed from the GLL equation and demonstrates its impact on bound states in a spherical well potential.

Findings

Rest energy can be eliminated under specific conditions.

Bound state spectrum is affected by rest energy when conditions are not met.

Number and energies of bound states depend on rest energy value.

Abstract

The generalized Levy-Leblond equation (GLL) is used to study the bound state problem for a non-relativistic Fermi field in external potentials. A condition when the rest energy term can be removed from the GLL equation is determined. For external potentials which do not obey the condition, the bound state spectrum is affected non-trivially by the rest energy of the Fermi field. This is demonstrated for a spherical finite-depth well potential. The existence, number, and energies of bound states depend on the value of the rest energy.