Vector coherent states with matrix moment problems

Details Vector coherent states with matrix moment problems Vector coherent states with matrix moment problems

2003-11-25

arxiv.org/abs/math-ph/0311046v3

J. Phys. A: Math. Gen. 37 (2004) 9531-9548

Physics

Mathematical Physics

18 pages

Scientific paper

10.1088/0305-4470/37/40/014

Canonical coherent states can be written as infinite series in powers of a single complex number $z$ and a positive integer $\rho(m)$. 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 $\{\rho(m)\}_{m=0}^\infty$. In this paper we obtain new classes of vector coherent states by simultaneously replacing the complex number $z$ and the moments $\rho(m)$ 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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