Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy bounds for the spinless Salpeter equation   We study the spectrum of the spinless-Salpeter Hamiltonian H = \beta
\sqrt{m^2 + p^2} + V(r), where V(r) is an attractive central potential in three
dimensions. If V(r) is a convex transformation of the Coulomb potential -1/r
and a concave transformation of the harmonic-oscillator potential r^2, then
upper and lower bounds on the discrete eigenvalues of H can be constructed,
which may all be expressed in the form E = min_{r>0} [ \beta \sqrt{m^2 +
P^2/r^2} + V(r) ] for suitable values of P here provided. At the critical point
the relative growth to the Coulomb potential h(r)=-1/r must be bounded by dV/dh
< 2\beta/\pi.

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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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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: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys