Year: 2008
Type: article
Abstract: We construct a new model of the quantum oscillator, whose energy spectrum is equally-spaced and lower-bound, whereas the spectra of position and of momentum are a denumerable non-degenerate set of points in [− 1, 1] that depends on the deformation parameter q ∊ (0, 1). We provide its explicit wavefunctions, both in position and momentum representations, in terms of the discrete q -Hermite polynomials. We build a Hilbert space with a unique measure, where an analogue of the fractional Fourier transform is defined in order to govern the time evolution of this discrete oscillator. In the limit when q → 1 − , one recovers the ordinary quantum harmonic oscillator.
Authors: Natig M Atakishiyev, Anatoliy U Klimyk, Kurt Bernardo Wolf
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1982954385