Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonunique C operator in PT Quantum Mechanics   The three simultaneous algebraic equations, $C^2=1$, $[C,PT]=0$, $[C,H]=0$,
which determine the $C$ operator for a non-Hermitian $PT$-symmetric Hamiltonian
$H$, are shown to have a nonunique solution. Specifically, the $C$ operator for
the Hamiltonian $H={1/2}p^2+{1/2}\mu^2q^2+i\epsilon q^3$ is determined
perturbatively to first order in $\epsilon$ and it is demonstrated that the $C$
operator contains an infinite number of arbitrary parameters. For each
different $C$ operator, the corresponding equivalent isospectral
Dirac-Hermitian Hamiltonian $h$ is calculated.

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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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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: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an