Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extension Of Bertrand's Theorem And Factorization Of The Radial
  Schr\"odinger Equation   The Bertrand's theorem is extended, i.e. closed orbits still may exist for
other central potentials than the power law Coulomb potential and isotropic
harmonic oscillator. It is shown that for the combined potential
$V(r)=W(r)+b/r^2$ ($W(r)=ar^{\nu}$), when (and only when) $W(r)$ is the Coulomb
potential or isotropic harmonic oscillator, closed orbits still exist for
suitable angular momentum. The correspondence between the closeness of
classical orbits and the existence of raising and lowering operators derived
from the factorization of the radial Schr\"odinger equation is investigated.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph