Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weber equation as a normal form with applications to top of the
  barrier scattering   In the paper we revisit the basic problem of tunneling near a nondegenerate
global maximum of a potential on the line. We reduce the semiclassical
Schr\"odinger equation to a Weber normal form by means of the Liouville-Green
transform. We show that the diffeomorphism which effects this stretching of the
independent variable lies in the same regularity class as the potential
(analytic or infinitely differentiable) with respect to both variables, i.e.,
space and energy. We then apply the Weber normal form to the scattering problem
for energies near the potential maximum. In particular we obtain a
representation of the scattering matrix which is accurate up to multiplicative
factors of the form 1 + o(1).

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The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ