Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A numerical study of the Schrodinger-Newton equation 1: Perturbing the
  spherically-symmetric stationary states   We consider the linear stability of the spherically-symmetric stationary
solutions of the Schrodinger-Newton equations. We find that the ground state is
linearly stable, with only imaginary eigenvalues, while the n-th excited state
has n quadruples of complex eigenvalues as well as purely imaginary ones and so
is linearly unstable.

24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph