Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diophantine approximation and the solubility of the Schroedinger
  equation   We characterise the set of periods for which number theoretical obstructions
prevent us from finding periodic solutions of the Schroedinger equation on a
two dimensional torus as well as the asymptotic occurrence of possible
resonances.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph