Degeneracy #
When the energy eigenvalues are the same but the eigenfunctions are different, it is referred to as being degenerate.
Fermi Energy #
The Fermi energy is the maximum energy that an electron can have at absolute zero.
$$E_F(0)=\frac{\hslash ^2}{2m}(3\pi ^2n)^{2/3}$$Here, \(n \equiv N/L^3\) is the number of electrons per unit volume, that is, the electron density.
At absolute zero, all energy levels below this energy value are filled with electrons, and the energy levels above it are empty.
Fermi Temperature #
$$T_F \equiv \frac{E_F(0)}{k}$$This is called the Fermi temperature. Here, \(k\) is the Boltzmann constant.
Fermi Velocity #
$$v_F=\Bigg(\frac{2E_F(0)}{m}\Bigg)^{1/2}$$This is called the Fermi velocity.