Generalized Squeezed States from Generalized Coherent States

TL;DR

This paper introduces a method to construct generalized minimum-uncertainty squeezed states for quantum systems beyond the harmonic oscillator, expanding the understanding of squeezed states in quantum mechanics.

Contribution

It proposes a new approach for deriving generalized minimum-uncertainty squeezed states and discusses their relation to existing concepts, addressing gaps in the understanding of displacement-operator squeezed states.

Findings

A method for obtaining generalized minimum-uncertainty squeezed states.

Examples illustrating the proposed method.

Discussion on the concept of displacement-operator squeezed states.

Abstract

Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the 1) displacement operator, 2) annihilation- (or ladder-) operator, and minimum-uncertainty methods. For general systems, there is the same understanding except for ladder-operator and displacement-operator squeezed states. After reviewing the known concepts, I propose a method for obtaining generalized minimum-uncertainty squeezed states, give examples, and relate it to known concepts. I comment on the remaining concept, that of general displacement-operator squeezed states.