Approach of the associated Laguerre functions to the su(1,1) coherent states for some quantum solvable models |
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Authors: | H Fakhri A Dehghani B Mojaveri |
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Institution: | 1. Faculty of Physics, Department of Theoretical Physics and Astrophysics, University of Tabriz, P. O. Box 51666‐16471, Tabriz, Iran;2. Faculty of Science, Department of Physics, Razi University, Kermanshah, Iran |
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Abstract: | Using second‐order differential operators as a realization of the su(1,1) Lie algebra by the associated Laguerre functions, it is shown that the quantum states of the Calogero‐Sutherland, half‐oscillator and radial part of a 3D harmonic oscillator constitute the unitary representations for the same algebra. This su(1,1) Lie algebra symmetry leads to derivation of the Barut‐Girardello and Klauder‐Perelomov coherent states for those models. The explicit compact forms of these coherent states are calculated. Also, to realize the resolution of the identity, their corresponding positive definite measures on the complex plane are obtained in terms of the known functions. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 |
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Keywords: | coherent states associated Laguerre functions quantum mechanics su(1 1) lie algebra |
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