Construction of coherent states for physical algebraic systems

TL;DR

This paper develops a method to construct coherent states for various algebraic systems by defining a general eigenvector of the annihilation operator, applicable across different energy spectra.

Contribution

It introduces a unified approach to generate coherent states for systems described by the Generalized Heisenberg Algebra, satisfying Klauder's conditions.

Findings

Constructed a general eigenvector for the annihilation operator.

Demonstrated applicability to multiple systems with different spectra.

Showed the states meet minimal coherence conditions.

Abstract

We construct a general state which is an eigenvector of the annihilation operator of the Generalized Heisenberg Algebra. We show for several systems, which are characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder's minimal coherent states.