Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic calculations for spectrum of superintegrable system from
  exceptional orthogonal polynomials   We introduce an extended Kepler-Coulomb quantum model in spherical
coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in
these coordinates and it is shown that the wave functions of the system can be
expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of
hypergeometric type). We construct ladder and shift operators based on the
corresponding wave functions and obtain their recurrence formulas. These
recurrence relations are used to construct higher-order, algebraically
independent integrals of motion to prove superintegrability of the Hamiltonian.
The integrals form a higher rank polynomial algebra. By constructing the
structure functions of the associated deformed oscillator algebras we derive
the degeneracy of energy spectrum of the superintegrable system.

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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess