Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exact solution method for 1D polynomial Schr\"odinger equations   Stationary 1D Schr\"odinger equations with polynomial potentials are reduced
to explicit countable closed systems of exact quantization conditions, which
are selfconsistent constraints upon the zeros of zeta-regularized spectral
determinants, complementing the usual asymptotic (Bohr--Sommerfeld)
constraints. (This reduction is currently completed under a certain vanishing
condition.) In particular, the symmetric quartic oscillators are admissible
systems, and the formalism is tested upon them. Enforcing the exact and
asymptotic constraints by suitable iterative schemes, we numerically observe
geometric convergence to the correct eigenvalues/functions in some test cases,
suggesting that the output of the reduction should define a contractive
fixed-point problem (at least in some vicinity of the pure $q^4$ case).

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
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The categories of this paper are: econ
25
The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
19
The categories of this paper are: eess