Vector coherent states and intertwining operators

TL;DR

This paper presents a general method for constructing vector coherent states of the Gazeau-Klauder type and explores their use in building isospectral and non-isospectral Hamiltonians through intertwining operators.

Contribution

It introduces a novel strategy for creating vector coherent states and extends intertwining operator techniques to generate isospectral and non-isospectral Hamiltonians.

Findings

Constructed vector coherent states of the Gazeau-Klauder type.

Developed a method to build isospectral Hamiltonians.

Explored the possibility of non-isospectral Hamiltonians with related eigenstates.

Abstract

In this paper we discuss a general strategy to construct vector coherent states of the Gazeau-Klauder type and we use them to built up examples of isospectral hamiltonians. For that we use a general strategy recently proposed by the author and which extends well known facts on intertwining operators. We also discuss the possibility of constructing non-isospectral hamiltonians with related eigenstates.