Schr\"odinger equation with delta potential in superspace

TL;DR

This paper extends the Schr"odinger equation with delta potential into superspace, deriving explicit energy expressions and wave functions for specific super-dimensions using Fourier analysis.

Contribution

It introduces a superspace version of the Schr"odinger equation with delta potential, providing explicit solutions and energy formulas for certain super-dimensions.

Findings

Explicit energy expression for super-dimension M ≤ 1

Wave function derived for one commuting and 2n anti-commuting variables

Analysis using Fourier methods in superspace

Abstract

A superspace version of the Schr\"odinger equation with a delta potential is studied using Fourier analysis. An explicit expression for the energy of the single bound state is found as a function of the super-dimension M in case M is smaller than or equal to 1. In the case when there is one commuting and 2n anti-commuting variables also the wave function is given explicitly.