The Energy Distribution Function

The distribution function f(E) is the probability that a particle is in energy state E. The distribution function is a generalization of the ideas of discrete probability to the case where energy can be treated as a continuous variable. Three distinctly different distribution functions are found in nature. The term A in the denominator of each distribution is a normalization term which may change with temperature.

Identical but distinguishable particles.Identical indistinguishable particles with integer spin (bosons).Identical indistinguishable particles with half-integer spin (fermions).
Examples: Molecular speed distribution
Examples: Thermal radiation
Specific heat
Examples: Electrons in a metal
Conduction in semiconductor.
The distribution of energyBasic distribution functions
Index

Quantum statistics concepts

Applied statistics concepts

Kinetic theory concepts
 
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The Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution is the classical distribution function for distribution of an amount of energy between identical but distinguishable particles.

Besides the presumption of distinguishability, classical statistical physics postulates further that:

  • There is no restriction on the number of particles which can occupy a given state.
  • At thermal equilibrium, the distribution of particles among the available energy states will take the most probable distribution consistent with the total available energy and total number of particles.
  • Every specific state of the system has equal probability.
Classical applications of the Boltzmann distribution
Distribution functionsNumerical example
Index

Applied statistics concepts

Reference
Blatt
Ch. 11.
 
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Maxwell-Boltzmann Details

The Maxwell-Boltzmann distribution.Comments on developing Maxwell-Boltzmann distribution.
Index

Applied statistics concepts
 
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