Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The two lowest eigenvalues of the harmonic oscillator in the presence of
  a Gaussian perturbation   In this note we consider a one-dimensional quantum mechanical particle
constrained by a parabolic well perturbed by a Gaussian potential. As the
related Birman-Schwinger operator is trace class, the Fredholm determinant can
be exploited in order to compute the modified eigenenergies which differ from
those of the harmonic oscillator due to the presence of the Gaussian
perturbation. By taking advantage of Wang's results on scalar products of four
eigenfunctions of the harmonic oscillator, it is possible to evaluate quite
accurately the two lowest-lying eigenvalues as functions of the coupling
constant $\lambda$.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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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: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat