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Both Fermi–Dirac and Bose–Einstein become Maxwell–Boltzmann statistics at high temperature or at low concentration. Bose–Einstein statistics was introduced for photons in 1924 by Bose and generalized to atoms by Einstein in 1924–25. The expected number of particles in an energy state i for Bose–Einstein statistics is:
The thermodynamics of an ideal Bose gas is best calculated using the grand canonical ensemble.The grand potential for a Bose gas is given by: = = (). where each term in the sum corresponds to a particular single-particle energy level ε i; g i is the number of states with energy ε i; z is the absolute activity (or "fugacity"), which may also be expressed in terms of the chemical ...
Download as PDF; Printable version ... Photon statistics is the theoretical and experimental study of the statistical distributions ... the Bose-Einstein distribution ...
Bose first sent a paper to Einstein on the quantum statistics of light quanta (now called photons), in which he derived Planck's quantum radiation law without any reference to classical physics. Einstein was impressed, translated the paper himself from English to German and submitted it for Bose to the Zeitschrift für Physik , which published ...
Similarly the Bose–Einstein correlations between two neutral pions are somewhat stronger than those between two identically charged ones: in other words two neutral pions are “more identical” than two negative (positive) pions. The surprising nature of these special Bose–Einstein correlations effects made headlines in the literature. [5]
All known particles obey either Fermi–Dirac statistics or Bose–Einstein statistics. A particle's intrinsic spin always predicts the statistics of a collection of such particles and conversely: [3] integral-spin particles are bosons with Bose–Einstein statistics, half-integral-spin particles are fermions with Fermi–Dirac statistics.
Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics we use the Thomas–Fermi approximation (gas in a box) and go to the limit of a very large trap, and express the degeneracy of the energy states as a differential, and summations over states as integrals.
Satyendra Nath Bose FRS, MP [1] (/ ˈ b oʊ s /; [4] [a] 1 January 1894 – 4 February 1974) was an Indian theoretical physicist and mathematician.He is best known for his work on quantum mechanics in the early 1920s, in developing the foundation for Bose–Einstein statistics, and the theory of the Bose–Einstein condensate.