Coherent states, displaced number states and Laguerre polynomial states for su(1,1) Lie algebra

Details Coherent states, displaced number states and Laguerre polynomial states for su(1,1) Lie algebra Coherent states, displaced number states and Laguerre polynomial states for su(1,1) Lie algebra

2000-01-02

arxiv.org/abs/quant-ph/0001002v2

Int. J. Mod. Phys. B. 14(10)(2000)1093-1104.

Physics

Quantum Physics

16 pages, no figures, accepted by Int. J. Mod. Phy. B

Scientific paper

10.1142/S0217979200001084

The ladder operator formalism of a general quantum state for su(1,1) Lie algebra is obtained. The state bears the generally deformed oscillator algebraic structure. It is found that the Perelomov's coherent state is a su(1,1) nonlinear coherent state. The expansion and the exponential form of the nonlinear coherent state are given. We obtain the matrix elements of the su(1,1) displacement operator in terms of the hypergeometric functions and the expansions of the displaced number states and Laguerre polynomial states are followed. Finally some interesting su(1,1) optical systems are discussed.

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