Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Using mixed data in the inverse scattering problem   Consider the fixed-$\ell$ inverse scattering problem. We show that the zeros
of the regular solution of the Schr\"odinger equation, $r_{n}(E)$, which are
monotonic functions of the energy, determine a unique potential when the domain
of the energy is such that the $r_{n}(E)$ range from zero to infinity. This
suggests that the use of the mixed data of phase-shifts
  $\{\delta(\ell_0,k), k \geq k_0 \} \cup \{\delta(\ell,k_0), \ell \geq \ell_0
\}$, for which the zeros of the regular solution are monotonic in both domains,
and range from zero to infinity, offers the possibility of determining the
potential in a unique way.

37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th