Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sufficient conditions for the existence of bound states in a central
  potential   We show how a large class of sufficient conditions for the existence of bound
states, in non-positive central potentials, can be constructed. These
sufficient conditions yield upper limits on the critical value,
$g_{\rm{c}}^{(\ell)}$, of the coupling constant (strength), $g$, of the
potential, $V(r)=-g v(r)$, for which a first $\ell$-wave bound state appears.
These upper limits are significantly more stringent than hitherto known
results.

5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th