Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Maupertuis Principle   According to the Maupertuis principle, the movement of a classical particle
in an external potential $V(x)$ can be understood as the movement in a curved
space with the metric $g_{\mu\nu}(x)=2M[V(x)-E]\delta_{\mu\nu}$. We show that
the principle can be extended to the quantum regime, i.e., we show that the
wave function of the particle follows a Schr\"odinger equation in curved space
where the kinetic operator is formed with the {\it Weyl--invariant
Laplace-Beltrami} operator. As an application, we use DeWitt's recursive
semiclassical expansion of the time-evolution operator in curved space to
calculate the semiclassical expansion of the particle density
$\rho(x;E)=<x|\delta(E-\hat H)|x>$.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th