Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical analysis for Hamiltonian in the Born-Oppenheimer
  approximation   The purpose of this paper is to show that the operator \begin{equation*}
H\left(h\right) =-h^{2}\Delta_{x}-\Delta_{y}+V\left(x,y\right),
\end{equation*}% $V$ is continuous (or $V\in
L^{2}\left(\mathbb{R}_{x}^{n}\times \mathbb{R}%_{y}^{p}\right) $), and
$V\left(x,y\right) \rightarrow \infty $ as $% \left\Vert x\right\Vert
+\left\Vert y\right\Vert \rightarrow \infty,$ has purely discrete spectrum. We
give an application to the harmonic oscillator.

20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat