Supersymmetry Transformations for Delta Potentials

TL;DR

This paper explores how second-order supersymmetry transformations expand the ability to manipulate the spectrum of a one-dimensional free Hamiltonian with a delta function perturbation, compared to first-order methods.

Contribution

It demonstrates that second-order SUSY transformations provide enhanced spectral manipulation capabilities over first-order transformations for delta potential systems.

Findings

Second-order SUSY transformations increase spectral manipulation options.

Enhanced control over Hamiltonian spectra with second-order transformations.

Detailed analysis of SUSY partners for delta potential systems.

Abstract

We make a detailed study of the first and second-order SUSY partners of a one-dimensional free Hamiltonian with a singular perturbation proportional to a Dirac delta function. It is shown that the second-order transformations increase the spectral manipulation possibilities offered by the standard first-order supersymmetric quantum mechanics.