Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple mathematical formulation of the correspondence principle   In this paper we suggest a simple mathematical procedure to derive the
classical probability density of quantum systems via Bohr's correspondence
principle. Using Fourier expansions for the classical and quantum
distributions, we assume that the Fourier coefficients coincide for the case of
large quantum numbers $n$. We illustrate the procedure by analyzing the
classical limit for the quantum harmonic oscillator, although the method is
quite general. We find, in an analytical fashion, the classical distribution
arising from the quantum one as the zeroth order term in an expansion in powers
of Planck's constant. We interpret the correction terms as residual quantum
effects at the microscopic-macroscopic boundary.

14
The categories of this paper are: math-ph
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs