1210.7259 (S. Arjika et al.)

$W_{(α,β)}^{ν,γ}(p, q)$-deformed Witt algebra: induced
deformed oscillator, associated hypergeometric functions, deformed states and
matrix elements    [PDF]

S. Arjika, D. Ousmane Samary, E. Baloïtcha, M. N. Hounkonnou

This work addresses a generalization of the Witt algebra, called $W_{(\alpha,\beta)}^{\nu,\gamma} (p, q)-$ deformed Witt algebra. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicitanalytic expressions of the energy spectrum are given. Deformed states are built and discussed with respect to the criteria of coherent state construction. Various commutators involving annihilation and creation operators and their combinatorics are computed and analyzed for both negative and nonnegative integers, engendering new classes of hypergeometric functions. Finally, the correlation functions of matrix elements of main normal and antinormal forms, pertinent for quantum optics analysis, are computed.

View original: http://arxiv.org/abs/1210.7259