Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Example of quantum systems reduction   To solve the quantum-mechanical problem the procedure of mapping onto linear
space $W$ of generators of the (sub)group violated by given classical
trajectory is formulated. The formalism is illustrated by the plane H-atom
model. The problem is solved noting conservation of the Runge-Lentz vector $n$
and reducing the 4-dimensional incident phase space $T$ to the 3-dimensional
linear subspace $W=T^* V\times R^1$, where $T^* V$ is the (angular momentum
($l$) - angle ($\vp$)) phase space and $R^1 =n$. It is shown explicitly that
(i) the motion in $R^1$ is pure classical as the consequence of the reduction,
(ii) motion in the $\vp$ direction is classical since the Kepler orbits are
closed independently from initial conditions and (iii) motion in the $l$
direction is classical since all corresponding quantum corrections are defined
on the bifurcation line ($l=\infty$) of the problem. In our terms the H-atom
problem is exactly quasiclassical and is completely integrable by this reasons.

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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg