We will now consider the derivation of the distribution function for free bosons carrying out the counting of states along the lines of what we did for the Maxwell-Boltzmann distribution. Let us start...We will now consider the derivation of the distribution function for free bosons carrying out the counting of states along the lines of what we did for the Maxwell-Boltzmann distribution. Let us start by considering how we obtained the binomial distribution. We considered a number of particles and how they can be distributed among, say, K boxes. As the simplest case of this, consider two particles and two boxes. The ways in which we can distribute them are as shown below.
There are two kinds of particles from the point of view of statistics, bosons and fermions. The corresponding statistical distributions are called the Bose-Einstein distribution and the Fermi-Dirac di...There are two kinds of particles from the point of view of statistics, bosons and fermions. The corresponding statistical distributions are called the Bose-Einstein distribution and the Fermi-Dirac distribution. Bosons have the property that one can have any number of particles in a given quantum state, while fermions obey the Pauli exclusion principle which allows a maximum of only one particle per quantum state. Any species of particles can be put into one of these two categories.
