Deepening the vector coherent state analysis: Revisiting the harmonic oscillator

TL;DR

This paper explores advanced vector coherent states for 2D and 3D harmonic oscillators, providing a systematic classification and demonstrating their continuous deformability while maintaining solvability.

Contribution

It introduces a systematic method for generating and classifying solvable vector coherent states for higher-dimensional harmonic oscillators.

Findings

Classified VCS based on specific criteria.

Demonstrated continuous deformability of VCS classes.

Provided solvable states satisfying resolution of the identity.

Abstract

Vector coherent states (VCS) viewed as a generalization of ordinary coherent states for higher rank tensor Hilbert spaces are investigated. We consider a systematic way of generating classes of VCS which are solvable (i.e., in the present context, normalizable states satisfying a resolution of the identity) on the Hilbert space of 2D and 3D harmonic oscillators. Thanks to the type of construction, these VCS are classified according to specific criteria. Furthermore, in many cases, the found classes of VCS are continuously deformable one onto another, still remaining solvable.