Almost-zero-energy Eigenvalues of Some Broken Supersymmetric Systems

TL;DR

This paper introduces a straightforward method to approximate the ground state energy of quantum systems with broken supersymmetry, especially in asymmetric double-well potentials, with applications to fermion bound states in scalar backgrounds.

Contribution

It provides a new simple formula for estimating the ground state energy in broken supersymmetric quantum systems with asymmetric potentials.

Findings

Derived a concise formula for approximate ground state energy.

Applicable to fermion bound states in kink-antikink backgrounds.

Effective for small energy eigenvalues in broken supersymmetric systems.

Abstract

For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground state energy in an associated, well-separated, asymmetric double-well-type potential. Our discussion is also relevant for the analysis of the fermion bound state in the kink-antikink scalar background.