I'm supposed to show that the degeneracy of the energy levels of conduction electrons at fixed [itex]k_z[/tex] in zero magnetic field is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{2L_x L_y}{\pi \hbar ^2} m \mu _B B[/tex]

Where the energy levels of the electrons are of the form (approximation):

[tex] E_{n,n_z} = E_n(k_z)= \frac{\hbar ^2 k_z ^2}{2m} + (n+\frac{1}{2})2\mu _B B [/tex]

where n is a nonnegative integer and [itex]k_z=2\pi n_z /L_z[/tex] with [itex]n_z[/itex] an integer (positive, negative or 0). The volume under consideration is[itex]V=L_x L_y L_z[/itex]

Here's what I think, the degeneracy is in the quantum number n, which represents the angular momentum quantum number. So the degeneracy at zero magnetic field is equal to the maximum number of n. But what restricts n???

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Degeneracy conduction electrons

**Physics Forums | Science Articles, Homework Help, Discussion**