Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ladder operators for solvable potentials connected with exceptional
  orthogonal polynomials   Exceptional orthogonal polynomials constitute the main part of the
bound-state wavefunctions of some solvable quantum potentials, which are
rational extensions of well-known shape-invariant ones. The former potentials
are most easily built from the latter by using higher-order supersymmetric
quantum mechanics (SUSYQM) or Darboux method. They may in general belong to
three different types (or a mixture of them): types I and II, which are
strictly isospectral, and type III, for which k extra bound states are created
below the starting potential spectrum. A well-known SUSYQM method enables one
to construct ladder operators for the extended potentials by combining the
supercharges with the ladder operators of the starting potential. The resulting
ladder operators close a polynomial Heisenberg algebra (PHA) with the
corresponding Hamiltonian. In the special case of type III extended potentials,
for this PHA the k extra bound states form k singlets isolated from the higher
excited states. Some alternative constructions of ladder operators are
reviewed. Among them, there is one that combines the state-adding and
state-deleting approaches to type III extended potentials (or so-called
Darboux-Crum and Krein-Adler transformations) and mixes the k extra bound
states with the higher excited states. This novel approach can be used for
building integrals of motion for two-dimensional superintegrable systems
constructed from rationally-extended potentials.

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The categories of this paper are: physics
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat