1
$\begingroup$

In Sommerfeld theory for metals, after determining all of the possible levels for a single electron, one says that we build up a state for a system with $N$ electrons by filling up those levels, beginning from that which has the lower energy to those which have more energy, in a crescent way. In fact, one call this configuration a Fermi sphere.

My question is: once a level is an eigenstate for the Hamiltonian operator of the problem, why can not the electrons be each one at any random level (respecting, of course, Pauli Exclusion's Principle), not necessarily making a Fermi sphere?

$\endgroup$
1
  • $\begingroup$ Because the Fermi sphere is lowest energy. $\endgroup$
    – Ron Maimon
    Aug 8, 2012 at 8:02

2 Answers 2

4
$\begingroup$

The Fermi level is supposed to be the highest occupied state at zero temperature. For fermions at zero temperature, they fill up these states with multiplicity one starting with the ground state up to the Fermi level. This is the lowest energy configuration that abides Pauli exclusion.

At positive temperature (or quantum mechanically) the fermions can be in any state.

$\endgroup$
-1
$\begingroup$

Fermi sphere is a sphere enclosing the occupied electron orbitals in the $K$ space or the reciprocal space at ground state (absolute temperature).

$\endgroup$
1
  • $\begingroup$ Ok, but why can not the electrons be each one at any random level, not necessarily making a Fermi sphere? $\endgroup$ Mar 29, 2017 at 17:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.