Coherent States of su(1,1): Correlations, Fluctuations, and the Pseudoharmonic Oscillator

Abstract

We extend recent results on expectation values of coherent oscillator states and SU(2) coherent states to the case of the discrete representations of su(1,1). Systematic semiclassical expansions of products of arbitrary operators are derived. In particular, the leading order of the energy uncertainty of an arbitrary Hamiltonian is found to be given purely in terms of the time dependence of the classical variables. The coherent states considered here include the Perelomov-Gilmore coherent states. As an important application we discuss the pseudoharmonic oscillator and compare the Perelomov-Gilmore states with the states introduced by Barut and Girardello. The latter ones turn out to be closer to the classical limit as their relative energy variance decays with the inverse square root of energy, while in the former case a constant is approached.

15 pages,1 figure. Typos corrected. References added, pertaining adjustments. Short discussion of the irregular eigenfunctions of the pseudoharmonic oscillator. Version to appear in J. Phys. A: Math. Theor

References in corpus (2)

• Generalized $su(1,1)$ coherent states for pseudo harmonic oscillator and their nonclassical properties
• Coherent Quantum Dynamics: What Fluctuations Can Tell

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