Itinerant States in the Fermi-Dirac Statistics

In a scheme of available energy states, a population of electrons distributes according the Fermi-Dirac statistics The probability f(E) of having an electron in a state of energy E, is, at temperature T 

The function f(E) is a step function for metals at 0 K electrons fill all states up to a well defined energy value Ep, which is called the Fermi energy of the solid. 

The Fermi level is the chemical potential gp of the electron population It may vary when the thermodynamic variables of the system are varied, e.g. temperature and 

2 This is not due, however, to the orthogonality constraint between 4 f and 5 f orbitals, contrary to a general belief (private communication from J. P. Desclaux) 

Its position in energy is determined by an integral equation such as  

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