Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete quantum model of the harmonic oscillator   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.

33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg