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Part 5: The Bose-Einstein Distribution

PHYS393 Statistical PhysicsPart 5: The Bose-Einstein DistributionDistinguishable and indistinguishable particlesIn the previous parts of this course, we derived the Boltzmanndistribution, which described how the number ofdistinguishableparticles in different energy states varied with the energy ofthose states, at different temperatures:nj=NZe jkT.(1)However, in systems consisting of collections of identicalfermions or identical bosons, the wave function of the systemhas to be either antisymmetric (for fermions) or symmetric (forbosons) under interchange of any two particles. With theallowed wave functions, it is no longer possible to identify aparticular particle with a particular energy state. Instead, allthe particles are shared between the occupied states.

appears in the expression for the Bose-Einstein distribution. This quantity corresponds to the partition function in the Boltzmann distribution, or the chemical potential in the Fermi-Dirac distribution. Bis determined by the constraint: X i ni= N, (25) where N is the total number of particles. Let us find how B depends on temperature.

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