Fermi Energy

E_F = \frac{\hbar^2}{2m}(3\pi^2 n)^{2/3}

The highest occupied energy level at absolute zero for a system of fermions. Crucial for understanding metals, white dwarfs, and neutron stars.

Variables

E_F

Fermi energy

\hbar

Reduced Planck constant

J·s

Particle mass (e.g., electron)

Number density of particles

m⁻³

Derived from counting quantum states up to the Fermi level in a free electron gas.

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