Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact wave functions for concentric two-electron systems   We show that the exact solution of the Schr\"odinger equation for two
electrons confined to two distinct concentric rings or spheres can be found in
closed form for particular sets of the ring or sphere radii. In the case of two
concentric rings, we report exact polynomial and irrational solutions. The same
methodology is applied to the case of two concentric spheres for which we
report exact polynomial solutions for the ground state and the excited states
of $S$ symmetry. For these concentric systems, we show that the exact wave
function does not contain terms proportional to the interelectronic distance
due to the spatial separation of the electrons.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys