Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic oscillator with nonzero minimal uncertainties in both position
  and momentum in a SUSYQM framework   In the context of a two-parameter $(\alpha, \beta)$ deformation of the
canonical commutation relation leading to nonzero minimal uncertainties in both
position and momentum, the harmonic oscillator spectrum and eigenvectors are
determined by using techniques of supersymmetric quantum mechanics combined
with shape invariance under parameter scaling. The resulting supersymmetric
partner Hamiltonians correspond to different masses and frequencies. The
exponential spectrum is proved to reduce to a previously found quadratic
spectrum whenever one of the parameters $\alpha$, $\beta$ vanishes, in which
case shape invariance under parameter translation occurs. In the special case
where $\alpha = \beta \ne 0$, the oscillator Hamiltonian is shown to coincide
with that of the q-deformed oscillator with $q > 1$ and its eigenvectors are
therefore $n$-$q$-boson states. In the general case where $0 \ne \alpha \ne
\beta \ne 0$, the eigenvectors are constructed as linear combinations of
$n$-$q$-boson states by resorting to a Bargmann representation of the latter
and to $q$-differential calculus. They are finally expressed in terms of a
$q$-exponential and little $q$-Jacobi polynomials.

34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex