A coherent state associated with shape-invariant potentials

TL;DR

This paper introduces a new algebraic approach to shape-invariant potentials, enabling the definition of a coherent state linked to these potentials through a generalized algebraic structure.

Contribution

It presents a novel algebraic framework connecting shape-invariance with a generalized Heisenberg-Weyl algebra, leading to the definition of associated coherent states.

Findings

Shape-invariance condition relates to a generalized Heisenberg-Weyl algebra.

A new operator reparametrizes wavefunctions to establish this connection.

Coherent states associated with shape-invariant potentials are constructed.

Abstract

An algebraic treatment of shape-invariant potentials is discussed. By introducing an operator which reparametrizes wavefunctions, the shape-invariance condition can be related to a generalized Heisenberg- Weyl algebra. It is shown that this makes it possible to define a coherent state associated with the shape-invariant potentials.