Historical Prospective: Boltzmann’s versus Planck’s State Counting—Why Boltzmann Did Not Arrive at Planck’s Distribution Law

Peter Enders1,2

1Technical University of Applied Sciences Wildau, Hochschulring 1, 15745 Wildau, Germany
2Kazakh National Pedagogical Abai University, Dostyk avenue 13, Almaty 050010, Kazakhstan

Received 7 August 2015; Accepted 11 November 2015

Abstract

Why does Planck (1900), referring to Boltzmann’s 1877 probabilistic treatment, obtain his quantumdistribution function while Boltzmann did not? To answer this question, both treatments are compared on the basis of Boltzmann’s 1868 three-level scheme (configuration—occupation—occupancy). Some calculations by Planck (1900, 1901, and 1913) and Einstein (1907) are also sketched. For obtaining a quantum distribution, it is crucial to stick with a discrete energy spectrum and to make the limit transitions to infinity at the right place. For correct state counting, the concept of interchangeability of particles is superior to that of indistinguishability.

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