A simple mathematical formulation of the correspondence principle

2011/01/06 by J. Bernal, Bernal, J., Alberto Martín-Ruiz +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1101.1242

9 pages

arxiv created 2012/09/15 · arxiv updated 2012/09/18

Abstract

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.

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