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

P. Enders | Zendy

Open Access

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

Author(s) -

P. Enders

Publication year - 2016

Publication title -

journal of thermodynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.112

H-Index - 11

eISSN - 1687-9252

pISSN - 1687-9244

DOI - 10.1155/2016/9137926

Subject(s) - boltzmann constant , planck , boltzmann distribution , physics , planck energy , einstein , statistical physics , maxwell–boltzmann distribution , state (computer science) , quantum mechanics , distribution function , distribution (mathematics) , quantum , theoretical physics , mathematics , electron , planck scale , quantum gravity , mathematical analysis , algorithm

Why does Planck (1900), referring to Boltzmann’s 1877 probabilistic treatment, obtain his quantum distribution 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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