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Approach of the associated Laguerre functions to the su (1,1) coherent states for some quantum solvable models
Author(s) -
Fakhri H.,
Dehghani A.,
Mojaveri B.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21944
Subject(s) - laguerre polynomials , coherent states , realization (probability) , unitary state , harmonic oscillator , mathematics , quantum , unitary representation , lie algebra , quantum algebra , algebra over a field , ladder operator , mathematical physics , symmetry (geometry) , quantum mechanics , physics , pure mathematics , lie group , current algebra , extension (predicate logic) , geometry , compact operator , programming language , statistics , political science , computer science , law
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