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arXiv:0904.0201 · Journal of Physics A Mathematical and Theoretical

Vector coherent states and intertwining operators

F Bagarello

Published Jan 21, 2009• 18 citations
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Abstract

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

DOI
10.1088/1751-8113/42/7/075302

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In this paper, we discuss a general strategy to construct vector coherent states of the Gazeau–Klauder type and we use them to build up examples of isospectral Hamiltonians. For that we use a general strategy recently proposed by the author, which extends well-known facts on intertwining operators. We also discuss the possibility of constructing non-isospectral Hamiltonians with related eigenstates.
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 In a recent paper, [1], we have proposed a new procedure which gives rise, given few ingredients, to a hamiltonian h2 which has the same spectrum of a given hamiltonian h1 and whose respective eigenstates are related by a given intertwining operator. These results extend what was discussed in the previous literature on this subject, [2], and have
In the spirit of some earlier work on the construction of vector coherent states (VCS) over matrix domains, we compute here such states associated to some physical Hamiltonians. In particular, we construct vector coherent states of the Gazeau–Klauder type. As a related problem, we also suggest a way to handle degeneracies in the Hamiltonian for building coherent states. Specific physical Hamiltonians studied include a single photon mode interacting with a pair of fermions, a Hamiltonian involving a single boson and a single fermion, a charged particle in a three-dimensional harmonic force field and the case of a two-dimensional electron placed in a constant magnetic field, orthogonal to the plane which contains the electron. In this last example, which is related to the fractional quantum Hall effect, an interesting modular structure emerges for two underlying von Neumann algebras, related to opposite directions of the magnetic field. This leads to the existence of coherent states built out of Kubo-Martin-Schwinger (KMS) states for the system.