A simple derivation of distribution functions for Bose and Fermi statistics

Dragoş-Victor Anghel

Robert F. O’Connell, Eugene Paul Wigner

Mo‐Lin Ge, Gang Su

By using the double-time Green function technique, the authors derive explicitly the exact statistical distribution function of the q-deformed harmonic oscillator, and find that it is highly different from the usual Bose and Fermi functions for q not=1.

Morikazu TODA, Fumihiko TAKANO

Michael J. R. Hoch

In nature, two different classes of particles are found, called fermi particles, or fermions, and bose particles, or bosons, respectively. The MB statistics is therefore an approximation to the true particle statistics and is applicable only in situations when most states are empty with some states occupied by a single particle and very few states, in the case of bosons, occupied by more than one particle. At high temperatures, the chemical potential decreases and the distribution changes its form dramatically. In discussing the quantum distribution functions, the authors have for convenience chosen the lowest state to have energy zero. The quantum distribution functions derived in this chapter are extremely useful in many areas of physics whenever what are called degenerate Fermi or Bose fluids are considered.

L.D. LANDAU, E.M. LIFSHITZ