Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darboux transformations for quasi-exactly solvable Hamiltonians   We construct new quasi-exactly solvable one-dimensional potentials through
Darboux transformations. Three directions are investigated:
  Reducible and two types of irreducible second-order transformations. The
irreducible transformations of the first type give singular intermediate
potentials and the ones of the second type give complex-valued intermediate
potentials while final potentials are meaningful in all cases.
  These developments are illustrated on the so-called radial sextic oscillator.

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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an