Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hermite function solutions of the Schr\"odinger equation for the sextic
  oscillator   We examine the conditions under which the solution of the radial stationary
Schr\"odinger equation for the sextic anharmonic oscillator can be expanded in
terms of Hermite functions. We find that this is possible for an infinite
hierarchy of potentials discriminated by the parameter setting the strength of
the centrifugal barrier. The $N$'th member of the hierarchy involves $N$
solutions for $N$ generally different values of the energy. For a particular
member of the hierarchy, there exist infinitely many bound states with square
integrable wave functions, written in terms of the Hermite functions, which
vanish at the origin and at infinity. These bound states correspond to distinct
values of the parameter setting the strength of the harmonic term. We also
investigate connection with the polynomial solutions of the sextic oscillator
obtained from the formalism of quasi-exactly solvable potentials.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: stat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
9
The categories of this paper are: nlin
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The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat