Degenerate discrete energy spectra and associated coherent states
- Centre de Recherches Mathematiques et Departement de Mathematiques et de Statistique, Universite de Montreal, C.P. 6128, Succursale Centre-ville, Montreal, (Quebec) H3C 3J7 (Canada)
Generalized and Gaussian coherent states constructed for quantum system with degeneracies in the energy spectrum are compared with respect to some minimal definitions and fundamental properties they have to satisfy. The generalized coherent states must be eigenstates of a certain annihilation operator that has to be properly defined in the presence of degeneracies. The Gaussian coherent states are, in the particular harmonic oscillator case, an approximation of the generalized coherent states and so the localizability in phase space of the particle in those states is very good. For other quantum systems, this last property serves as a definition of those Gaussian coherent states. The example of a particle in a two-dimensional square box is thus revisited having in mind the preceding definitions of generalized and Gaussian coherent states and also the preservation of the important property known as the resolution of the identity operator.
- OSTI ID:
- 20929610
- Journal Information:
- Journal of Mathematical Physics, Vol. 48, Issue 1; Other Information: DOI: 10.1063/1.2435596; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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