Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectroscopy of annular drums and quantum rings: perturbative and
  nonperturbative results   We obtain systematic approximations to the states (energies and wave
functions) of quantum rings (annular drums) of arbitrary shape by conformally
mapping the annular domain to a simply connected domain. Extending the general
results of Ref.\cite{Amore09} we obtain an analytical formula for the spectrum
of quantum ring of arbirtrary shape: for the cases of a circular annulus and of
a Robnik ring considered here this formula is remarkably simple and precise. We
also obtain precise variational bounds for the ground state of different
quantum rings. Finally we extend the Conformal Collocation Method of
\cite{Amore08,Amore09} to the class of problems considered here and calculate
precise numerical solutions for a large number of states ($\approx 2000$).

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas