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Vector coherent states with matrix moment problems

K. Thirulogasanthar·A. L. Hohoueto
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Abstract

Canonical coherent states can be written as infinite series in powers of a single complex number $z$ and a positive integer $ρ(m)$. The requirement that these states realize a resolution of the identity typically results in a moment problem, where the moments form the positive sequence of real numbers $\{ρ(m)\}_{m=0}^\infty$. In this paper we obtain new classes of vector coherent states by simultaneously replacing the complex number $z$ and the moments $ρ(m)$ of the canonical coherent states by $n \times n$ matrices. Associated oscillator algebras are discussed with the aid of a generalized matrix factorial. Two physical examples are discussed. In the first example coherent states are obtained for the Jaynes-Cummings model in the weak coupling limit and some physical properties are discussed in terms of the constructed coherent states. In the second example coherent states are obtained for a conditionally exactly solvable supersymmetric radial harmonic oscillator.

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K. Thirulogasanthar, A. L. Hohoueto. 2004-09-02. Vector coherent states with matrix moment problems. https://doi.org/10.1088/0305-4470/37/40/014

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