Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely many shape invariant potentials and new orthogonal
  polynomials   Three sets of exactly solvable one-dimensional quantum mechanical potentials
are presented. These are shape invariant potentials obtained by deforming the
radial oscillator and the trigonometric/hyperbolic P\"oschl-Teller potentials
in terms of their degree \ell polynomial eigenfunctions. We present the entire
eigenfunctions for these Hamiltonians (\ell=1,2,...) in terms of new orthogonal
polynomials. Two recently reported shape invariant potentials of Quesne and
G\'omez-Ullate et al's are the first members of these infinitely many
potentials.

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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph