Mathematics – Logic
Scientific paper
Apr 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aps..apr.d1061k&link_type=abstract
American Physical Society, APS April Meeting, April 22-26, 2006, abstract #D1.061
Mathematics
Logic
Scientific paper
The critical analysis of Bose-Einstein statistics and Fermi-Dirac statistics---consequence of Bose's method---is proposed. The main result of the analysis is as follows. (1) In accordance with the definition, Bose-Einstein (B-E) and Fermi-Dirac (F-D) distribution functions f(B-E)^s , f(F-D)^s are the average values of the random quantity: f^s≡ɛ^s / ɛ^s ɛ1^s . - ɛ1^s , ɛ^s≡∑rɛr^s pr^s , pr^s =p0^s ,,[ -,α+βɛ1^s )r ]^, r=0,;1,;1pt(B-E), r=0,;1(F-D) where f^s is the average number of the noninteracting monoenergetic identical quantum particles in the s-layer cell; ɛ1^s is energy of one particle of kind s; pr^s is the probability that energy takes on the value ɛr^s =ɛ1^s r≡(α+βɛ1^s )r / (α+βɛ1^s )r β . - β; 1 / 1 β≡T . - β≡T is temperature; α≡-βμ is degeneration parameter; μ is chemical potential. (2) In accordance with the logic law of identity, pr^s ≡pr^s , ɛr^s =ɛ1^s r≡(α+βɛ1^s )r / (α+βɛ1^s )r β . - β. Hence, α≡0. Thus, μ≡0 and, consequently, Bose-Einstein statistics and Fermi-Dirac statistics represent logical error.
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