Coherent states for isospectral Hamiltonians

Abstract

We give a construction of coherent states for strictly isospectral Hamiltonians by exploiting the fact that these are related by a unitary transformation, and hence the corresponding coherent states must be related by the same unitary transformation. We give the explicit structure of such a unitary transformation in terms of the eigenvalues and eigenfunctions of a given factorizable Hamiltonian. As an illustration, we discuss the example of strictly isospectral one-dimensional harmonic oscillator Hamiltonians and the associated coherent states, and point out inadequacies in recent constructions of such coherent states in the literature.