Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Quantum Reduced Action In Higher Dimensions   The solution with respect to the reduced action of the one-dimensional
stationary quantum Hamilton-Jacobi equation is well known in the literature.
The extension to higher dimensions in the separated variable case was proposed
in contradictory formulations. In this paper we provide new insights into the
construction of the reduced action. In particular, contrary to the classical
mechanics case, we analytically show that the reduced action constructed as a
sum of one variable functions does not contain a complete information about the
quantum motion. In the same context, we also make some observations about
recent results concerning quantum trajectories. Finally, we will examine the
conditions in which microstates appear even in the case where the wave function
is complex.

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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th