Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Accuracy of Semiclassical Quantization for Integrable Systems   The eigenvalues of the Hyperspherical billiard are calculated in the
semiclassical approximation. The eigenvalues where this approximation fails are
identified and found to be related to caustics that approach the wall of the
billiard. The fraction of energy levels for which the semiclassical error is
larger than some given value is calculated analytically (and tested
numerically) and found to be independent of energy. The implications for other
systems, in particular integrable ones, are discussed.

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The categories of this paper are: cs
25
The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
0
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: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat