Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PT-symmetric eigenvalues for homogeneous potentials   We consider one-dimensional Schr\"odinger equations with homogeneous
potential, under appropriate PT-symmetric boundary conditions. We prove the
phenomenon which was discovered by Bender and Boettcher by numerical
computation: as the degree of the potential changes, the real spectrum suddenly
becomes non-real in the sense that all but finitely many eigenvalues become
non-real. We find the limit arguments of these non-real eigenvalues as they
tend to infinity.

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: stat