Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians

TL;DR

This paper introduces a distorted Heisenberg algebra linked to isospectral oscillator Hamiltonians, derives its coherent states, and discusses how to generate squeezing effects by initial state selection.

Contribution

It defines a new distorted Heisenberg algebra parameterized by w, extending the standard algebra for isospectral oscillators, and constructs associated coherent states.

Findings

The representation becomes similar to the standard Heisenberg algebra, dependent on parameter w.

Explicit coherent states are derived for arbitrary w.

A method to produce squeezing by initial state preparation is provided.

Abstract

The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of the standard Heisenberg algebra, and it is dependent of a parameter $w\geq 0$. We name it {\it distorted Heisenberg algebra}, where $w$ is the distortion parameter. The corresponding coherent states for an arbitrary $w$ are derived, and some particular examples are discussed in full detail. A prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.