Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bateman's dual system revisited: I. Quantization, geometric phase and
  relation with the ground-state energy of the linear harmonic oscillator   By using the Feynman-Hibbs prescription for the evolution amplitude, we
quantize the system of a damped harmonic oscillator coupled to its
time-reversed image, known as Bateman's dual system.
  The time-dependent quantum states of such a system are constructed and
discussed entirely in the framework of the classical theory.
  The corresponding geometric (Pancharatnam) phase is calculated and found to
be directly related to the ground-state energy of the 1D linear harmonic
oscillator to which the 2D system reduces under appropriate constraint.

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The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: math
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The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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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: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con