Supersymmetric Quantum Mechanics of Scattering

TL;DR

This paper introduces a supersymmetric quantum mechanics framework tailored for scattering states, which are typically represented by generalized functions outside the standard Hilbert space, enhancing the theoretical tools for collision problems.

Contribution

It proposes a novel supersymmetric quantum mechanics approach specifically designed for scattering states expressed as generalized functions.

Findings

Provides a new theoretical framework for scattering states

Extends supersymmetric quantum mechanics to non-Hilbert space states

Facilitates analysis of collision problems in quantum mechanics

Abstract

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed.