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Proceedings Paper

Q-extension of the linear harmonic oscillator
Author(s): Mesuma K. Atakishiyeva; Natig M. Atakishiyev; Carlos Villegas-Blas
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Paper Abstract

Overlap integrals over the full real line for a family of q- extensions of the linear harmonic oscillator wave functions in quantum mechanics are evaluated. In particular, an explicit form of the squared norms for these q-wave functions is obtained. The classical Fourier-Gauss transform connects the families with different values 0 < q < 1 and q < 1 of the deformation parameter q. An explicit expansion of the q-Hermite polynomials of Rogers in terms of the ordinary Hermite polynomials emerges as a by-product.

Paper Details

Date Published: 6 July 1998
PDF: 7 pages
Proc. SPIE 3385, Photonic Quantum Computing II, (6 July 1998); doi: 10.1117/12.312640
Show Author Affiliations
Mesuma K. Atakishiyeva, Univ. Autonoma del Estado de Morelos (Mexico)
Natig M. Atakishiyev, Univ. Nacional Autonoma de Mexico (Mexico)
Carlos Villegas-Blas, Univ. Nacional Autonoma de Mexico (Mexico)

Published in SPIE Proceedings Vol. 3385:
Photonic Quantum Computing II
Steven P. Hotaling; Andrew R. Pirich, Editor(s)

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