Fermi Dirac Statistics

• It is applied to Fermions or Fermi particles, i.e. indistinguishable particle with half integral spin.
• Particles are indistinguishable from each other.
• Each cell or sublevel may contain 0 or 1 particle i.e., g_i,  >> n_i
• 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

• Consider a system of n independent identical particles having half integral spin.
• 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 n_i particles among them.

• Number of ways to put first particle in any one of the i^ih  level = g_i 
• Number of ways to put second particle in the remaining (g_i  – 1) state = (g_i  – 1)

            …     …     …     …     …     …

• Total number of ways to distribute n_i  particles in g_i  states = g_i (g_i  – 1) (g_i  – 2) ... (g_i – n_i + 1)




• Sterling approximation log x! = x log x – x







To know about this lecture in more detail please visit on https://youtu.be/Tap561DKzIw