Recursive approach to supersymmetric quantum mechanics for arbitrary fermion occupation number

TL;DR

This paper introduces a recursive numerical method for solving supersymmetric quantum mechanics systems with gauge symmetry across all fermionic sectors, applicable to any gauge group, demonstrated on a supersymmetric anharmonic oscillator.

Contribution

It develops a recursive algorithm to compute matrix elements of gauge-invariant operators in any fermionic sector for supersymmetric quantum systems.

Findings

Method successfully applied to a supersymmetric anharmonic oscillator

Algorithm handles all fermionic sectors and gauge groups

Provides detailed numerical solutions for supersymmetric models

Abstract

We present in details a numerical approach for solving supersymmetric quantum mechanical systems with a gauge symmetry valid in all fermionic sectors. The method uses a recursive algorithm to calculate matrix elements of any gauge invariant operator in the Fock basis, in particular of the Hamiltonian operator, and can be used for any gauge group. We describe its application to a supersymmetric anharmonic oscillator model with discrete spectrum.