Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of ($\ell$-dependent) potentials with the same number of
  ($\ell$-wave) bound states   We introduce and investigate the class of central potentials
$$V_{\text{CIC}}(g^{2},\mu^{2},\ell,R;r)=-\frac{g^{2}}{R^{2}}
(\frac{r}{R})^{4\ell} {[ 1+(\frac{1}{2\ell+1})
(\frac{r}{R})^{2\ell+1}]^{2}-1+\mu^{2}}^{-2}$$, which possess, in the context
of nonrelativistic quantum mechanics, a number of $\ell$-wave bound states
given by the ($\ell$-independent !) formula $$N_{\ell}^{\text{(CIC)}}(g^{2},\mu
^{2}) ={{\frac{1}{\pi}\sqrt{g^{2}+\mu^{2}-1} (\sqrt{\mu^{2}-1})^{-1}
\arctan(\sqrt{\mu^{2}-1})}}$$. Here $g$ and $\mu$ are two arbitrary real
parameters, $\ell$ is the angular momentum quantum number, and the double
braces denote of course the integer part. An extension of this class features
potentials that possess the same number of $\ell$-wave bound states and behave
as $(a/r)^{2}$ both at the origin ($r\to 0^{+}$) and at infinity ($r\to
\infty$), where $a$ is an additional free parameter.

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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
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The categories of this paper are: funct-an