On the classical limit of quantum mechanics

Details On the classical limit of quantum mechanics On the classical limit of quantum mechanics

2011-01-06

arxiv.org/abs/1101.1242v5

Physics

Quantum Physics

8 pages

Scientific paper

In this paper, we suggest a simple mathematical procedure to connect the classical and quantum probability densities for both position and momentum via Bohr's correspondence principle. Using a Fourier expansion of the classical and quantum distribution, respectively, we postulate that the Fourier coefficients have a similar behavior for large quantum number $n$. We discuss the classical limit for two simple quantum systems. The most important result is the emergence of classical distribution, keeping Planck's constant non-zero. We interpret the correction terms ($\hbar$-dependent) as a residual effect of quantum behavior surviving at the classical level.

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