Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact quantization of nonsolvable potentials: the role of the quantum
  phase beyond the semiclassical approximation   Semiclassical quantization is exact only for the so called \emph{solvable}
potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the
semiclassical phase, given by a series in $\hbar$, yields more or less
approximate results and eventually diverges due to the asymptotic nature of the
expansion. A quantum phase is derived to bypass these shortcomings. It achieves
exact quantization of nonsolvable potentials and allows to obtain the quantum
wavefunction while locally approaching the best pre-divergent semiclassical
expansion. An iterative procedure allowing to implement practical calculations
with a modest computational cost is also given. The theory is illustrated on
two examples for which the limitations of the semiclassical approach were
recently highlighted: cold atomic collisions and anharmonic oscillators in the
nonperturbative regime.

27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin