# Numbers of electrons on the Fermi surface

#### Tianwu Zang

In free electron 3D box model, we can calculate the density of state on the Fermi surface g($$\epsilon$$f) easily, but how about the level spacing near the Fermi surface? I think this level spacing $$\Delta$$E should satisfy $$\Delta$$E=d/g($$\epsilon$$f) where d is the degree of degenerate on the Fermi surface. So how many electrons are on the Fermi surface? Are there only 6? ({kf,0,0,$$\uparrow$$};{kf,0,0,$$\downarrow$$};{0,kf,0,$$\uparrow$$};{0,kf,0,$$\downarrow$$};{0,0,kf,$$\uparrow$$};{0,0,kf,$$\downarrow$$})
In one textbook I saw level spacing near the Fermi surface is nearly $$\epsilon$$f/N, so how can d/g($$\epsilon$$f) be connected with $$\epsilon$$f/N?
Thank you so much :-)

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