Coherent states for polynomial su(1,1) algebra and a conditionally solvable system

Abstract

In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1,1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1,1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.

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References in corpus (5)

• Coherent States for the Hydrogen Atom
• Coherent States of Non-Linear Lie algebras: Application in Quantum Optics
• Non-linear coherent states associated with conditionally exactly solvable problems
• Quasi-classical path integral approach to supersymmetric quantum mechanics
• Klauder's coherent states for the radial Coulomb problem in a uniformly curved space and their flat-space limits

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• A polynomial class of $u(2)$ algebras