Equivalent sets of coherent states of the 1D infinite square well and properties

TL;DR

This paper proves the equivalence of two types of coherent states in the 1D infinite square well and derives approximate expressions for their probability densities, explaining their quasi-classical behavior analytically.

Contribution

It establishes the conditions under which two sets of coherent states are equivalent and provides analytical expressions to explore their properties.

Findings

Equivalence of generalized and Gaussian Klauder coherent states under certain conditions

Approximate analytical expressions for probability density and wave function

Explanation of quasi-classical behavior in terms of observables and uncertainty

Abstract

We prove the equivalence (under some conditions) of two sets of coherent states built for the one-dimensional infinite square well: the so-called generalized and Gaussian Klauder coherent states. We then derive an approximate close expression approaching their probability density and wave function to explore their properties analytically. This process gives thereby explanation of the quasi-classical behavior of these states in terms of the main observables and the Heisenberg uncertainty product