Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sampling The Lowest Eigenfunction to Recover the Potential in a
  One-Dimensional Schr\"odinger Equation   We consider the BVP $-y" + qy = \lambda y$ with $y(0)=y(1)=0$. The inverse
spectral problems asks one to recover $q$ from spectral information. In this
paper, we present a very simple method to recover a potential by sampling one
eigenfunction. The spectral asymptotics imply that for larger modes, more and
more information is lost due to imprecise measurements (i.e. relative errors
\textit{increases}) and so it is advantageous to use data from lower modes. Our
method also allows us to recover "any" potential from \textit{one} boundary
condition.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int