Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correct Small-Truncated Excited State Wave functions Obtained via
  Minimization Principle for Excited States compared / opposed to
  Hylleraas-Undheim and McDonald higher roots   We demonstrate that, if a truncated expansion of a wave function is Large,
then the standard excited states computational method, of optimizing one root
of a secular equation, according to the theorem of Hylleraas, Undheim and
McDonald (HUM), tends to the correct excited wave function, comparable to that
obtained via our proposed minimization principle for excited states [J. Comput.
Meth. Sci. Eng. 8, 277 (2008)] (independent of orthogonality to lower lying
approximants). However, if a truncated expansion of a wave function is Small -
that would be desirable for large systems - then the HUM-based methods may lead
to an incorrect wave function - despite the correct energy (: according to the
HUM theorem) whereas our method leads to correct, reliable, albeit Small
truncated wave functions. The demonstration is done in He excited states, using
truncated series Small expansions both in Hylleraas coordinates, and via
standard configuration-interaction truncated Small expansions, in comparison
with corresponding Large expansions. Beyond that, we give some examples of
linear combinations of Hamiltonian eigenfunctions that have the energy of the
1st excited state, albeit they are orthogonal to it, demonstrating that the
correct energy is not a criterion of correctness of the wave function.

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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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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: q-alg
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The categories of this paper are: alg-geom