Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completeness theorem for the system of eigenfunctions of the complex
  Schr\"odinger operator $L=-d^2/dx^2+cx^{2/3}$   We prove the completeness of the system of eigenfunctions of the complex
Schr\"odinger operator $L=-d^2/dx^2+cx^{2/3}$ on the semiaxis in
$L_2(0,+\infty)$ with Dirichlet boundary conditions for all $c$: $|\arg
c|<\pi/2+\theta_0$, where $\theta_0\in(\pi/10,\pi/9)$ is defined as the only
solution of a certain transcendental equation.

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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin