Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schr\"odinger Operators with Many Bound States   Consider the Schr\"odinger operators $H_{\pm}=-d^2/dx^2\pm V(x)$. We present
a method for estimating the potential in terms of the negative eigenvalues of
these operators. Among the applications are inverse Lieb-Thirring inequalities
and several sharp results concerning the spectral properties of $H_{\pm}$.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol