On (p, q, μ, ν, ϕ1, ϕ2)-generalized oscillator algebra and related bibasic hypergeometric functions

Abstract

This paper provides the generalization of the work by Floreanini et al (1993 J. Phys. A: Math. Gen. 26 611–4) who generated bibasic hypergeometric functions from (p, q)-oscillators. We consider a six-parameter deformed oscillator algebra realized from the (p, q)-deformed boson oscillators. We build the corresponding Fock space representation in an infinite-dimensional subspace of the Hilbert space of a harmonic oscillator. We also discuss the properties of a discrete spectrum of the Hamiltonian of the deformed harmonic oscillator corresponding to this system. We then define a realization of the deformed algebra in terms of a generalized derivative and investigate the relation between this representation and generalized bibasic Laguerre functions and polynomials.