Bose Einstein Statistics

• It is applied to Boson or Bose particles, i.e. indistinguishable particle with integral spin
• Particles are indistinguishable from each other.
• Each cell of i^th  quantum state may contain 0, 1, 2, …, n_i  particles.
• Total number of particles of system remain constant, n = Σn_i  = constant
• Sum of energies of all the particles in the different groups taken together i.e., total energy of the system remain constant E = Σn_iε_i  = constant
• Particles are indistinguishable from each other.

• Consider a system of n independent identical particles.
• These particles be divided into quantum groups or levels such that
• Energy levels    ε_1, ε_2, ε_{3, ...}ε_i 
• Degeneracies    g_1, g_2, g_{3, ...}g_i 
• Occupation number    n_1, n_2, n_{3, ...}n_i 

• Consider a box, divide it into g_i  sections, distribute particles among them.

• There are g_i  ways to choose the sequence of compartments.
• After it remaining (g_i  – 1) compartment and n_i  particles i.e., total (n_i  + g_i  – 1) particles can be arranged by (n_i  + g_i  – 1)!
• Total number of ways of distribution = g_i (n_i  + g_i  – 1)!

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