Q-extension of the linear harmonic oscillator

Mesuma K. Atakishiyeva; Natig M. Atakishiyev; Carlos Villegas-Blas

doi:10.1117/12.312640

6 July 1998 Q-extension of the linear harmonic oscillator

Mesuma K. Atakishiyeva, Natig M. Atakishiyev, Carlos Villegas-Blas

Proceedings Volume 3385, Photonic Quantum Computing II; (1998) https://doi.org/10.1117/12.312640
Event: Aerospace/Defense Sensing and Controls, 1998, Orlando, FL, United States

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.

Citation Download Citation

Mesuma K. Atakishiyeva, Natig M. Atakishiyev, and Carlos Villegas-Blas "Q-extension of the linear harmonic oscillator", Proc. SPIE 3385, Photonic Quantum Computing II, (6 July 1998); https://doi.org/10.1117/12.312640

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