Shape-invariant potentials and an associated coherent state

TL;DR

This paper develops an algebraic framework for shape-invariant potentials in supersymmetric quantum mechanics, enabling the construction of associated coherent states with resolution of unity for many such potentials.

Contribution

It introduces an operator that reparametrizes wave functions, linking shape-invariance to an oscillator-like algebra and defining new coherent states.

Findings

Coherent states with resolution of unity are constructed for a broad class of shape-invariant potentials.

An algebraic approach relates shape-invariance to oscillator-like algebra structures.

The method provides a systematic way to generate coherent states in supersymmetric quantum mechanics.

Abstract

An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like algebra. It makes possible to define a coherent state associated with the shape-invariant potentials. For a large class of such potentials, it is shown that the introduced coherent state has the property of resolution of unity.