A Simple Mathematical Formulation of the Correspondence Principle

J. Bernal, A. Martín-Ruiz, J. C. García-Melgarejo

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México D.F., México.
Instituto Nacional de Astrofísica, óptica y Electrónica, Santa María Tonantzintla, México.
Universidad Juárez Autónoma de Tabasco, División Académica de Ciencias Básicas, Cunduacán, México.

DOI: 10.4236/jmp.2013.41017                

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.

Keywords

Correspondence Principle; Classical Limits

Conflicts of Interest

The authors declare no conflicts of interest.

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