Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable quantum St\"ackel systems   The St\"ackel separability of a Hamiltonian system is well known to ensure
existence of a complete set of Poisson commuting integrals of motion quadratic
in the momenta. In the present paper we consider a class of St\"ackel separable
systems where the entries of the St\"ackel matrix are monomials in the
separation variables. We show that the only systems in this class for which the
integrals of motion arising from the St\"ackel construction keep commuting
after quantization are, up to natural equivalence transformations, the
so-called Benenti systems. Moreover, it turns out that the latter are the only
quantum separable systems (that is, they admit separation of variables in the
Schr\"odinger equation) in the class under study.

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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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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: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: dg-ga