Journal of Modern Physics
Volume 4, Issue 1 (January 2013)
ISSN Print: 2153-1196 ISSN Online: 2153-120X
Google-based Impact Factor: 0.86 Citations h5-index & Ranking
A Simple Mathematical Formulation of the Correspondence Principle ()
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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 number. We illustrate the procedure by analyzing the classical limit for the quantum harmonic oscillator and the particle in a box, 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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