Generalized Hypergeometric Coherent States

Abstract

We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disk, and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg-Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce generalized hypergeometric Husimi distributions and corresponding phase distributions as well as new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces.

12 pages, 13 figures

References in corpus (4)

• f-Oscillators and Nonlinear Coherent States
• Generalized Coherent States Associated with the $C_{\lambda }$-Extended Oscillator
• Generalized coherent states associated with the C_λ-extended oscillator
• Hypergeometric States and Their Nonclassical Properties

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• Extended Weyl-Heisenberg algebra, phase operator, unitary depolarizers and generalized Bell states
• Bicomplex generalized hypergeometric functions and their applications
• Aspects of coherent states of nonlinear algebras