A discrete quantum model of the harmonic oscillator
Por:
Atakishiyev N.M., Klimyk A.U., Wolf K.B.
Publicada:
29 feb 2008
Resumen:
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 is an element of ( 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.
Filiaciones:
Atakishiyev N.M.:
Univ Nacl Autonoma Mexico, Inst Matemat, Cuernavaca 62251, Morelos, Mexico
Klimyk A.U.:
Bogolyubov Institute for Theoretical Physics, Metrologichna 14b, Kiev 03143, Ukraine
Wolf K.B.:
Univ Nacl Autonoma Mexico, Inst Ciencias Fis, Cuernavaca 62251, Morelos, Mexico
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