Supersymmetric infinite wells and coherent states

TL;DR

This paper explores Gaussian Klauder coherent states in the infinite well quantum model and its supersymmetric partner, demonstrating their quasi-classical evolution, localization, and relation to generalized coherent states in one- and two-dimensional systems.

Contribution

It introduces a construction of coherent states for supersymmetric partner systems of the infinite well, showing they retain key properties of classical-like states.

Findings

States exhibit high localization and quasi-classical evolution

States approximately saturate Heisenberg uncertainty relation

Relations established between Gaussian and generalized coherent states

Abstract

Gaussian Klauder coherent states are discussed in the context of the infinite well quantum model, otherwise known as the particle in a box. A supersymmetric partner system is also presented, as well as a construction of coherent states in this new system. We show that these states can be chosen, in both systems to have many properties usually expected for coherent states. In particular, they yield highly localised wave packets for a short period of time, which evolve in a quasi-classical manner and which saturate approximately Heisenberg uncertainty relation. These studies are elaborated in one- and two-dimensional contexts. Finally, some relations are established between the gaussian states being mostly used here and the generalised coherent states, which are more standardly found in the literature.