Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Borel summability of WKB solutions of certain Schr\"odinger-type
  differential equations   A class of Schr\"odinger-type second-order linear differential equations with
a large parameter $u$ is considered. Analytic solutions of this type of
equations can be described via (divergent) formal series in descending powers
of $u$. These formal series solutions are called the WKB solutions. We show
that under mild conditions on the potential function of the equation, the WKB
solutions are Borel summable with respect to the parameter $u$ in large,
unbounded domains of the independent variable. It is established that the
formal series expansions are the asymptotic expansions, uniform with respect to
the independent variable, of the Borel re-summed solutions and we supply
computable bounds on their error terms. In addition, it is proved that the WKB
solutions can be expressed using factorial series in the parameter, and that
these expansions converge in half-planes, uniformly with respect to the
independent variable. We illustrate our theory by application to a radial
Schr\"odinger equation associated with the problem of a rotating harmonic
oscillator and to the Bessel equation.

22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci