तापमान T पर फर्मी कणों (Fermi particles) के एक आदर्श क्वांटम गैस पर विचार कीजिए। माध्य अधिभोग संख्या ⟨n⟩ (mean occupation number) के फलन के रूप में किसी दिए गए एकल कण अवस्था में n कण होने की प्रायिकता, p(n) क्या है?

A binary alloy consists of NA A-type and NB B-type atoms on a simple cubic lattice. Nearby neighbors interact with attractive energy -J (J > 0) between like pairs (AA or BB) and repulsive energy +J between unlike pairs (AB). If N is the total number of sites, the average energy of the system at high temperature (kBT ≫ J) is:

Consider a one-dimensional lattice (with lattice spacing a) along X-axis with sites labelled by x = 0, 1, 2, ..., L. A particle carrying charge -q can occupy any one of these sites. An electric field of strength E is applied in the positive x-direction. The average energy of the particle at temperature T (in the limit L → ∞) is (β = 1kB T):