Discrete quantum model of the harmonic oscillator

Autor:	Atakishiyev, Natig M., Klimyk, Anatoliy U., Wolf, Kurt Bernardo
Rok vydání:	2007
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8113/41/8/085201
Popis:	We construct a new model of the quantum oscillator, whose energy spectrum is equally-spaced and lower-bounded, whereas the spectra of position and momentum are a denumerable non-degenerate set of points in [-1,1] that depends on the deformation parameter q from (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 q to 1, one recovers the ordinary quantum harmonic oscillator. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0711.3089 Zobrazit plný text záznamu View this record from Arxiv