Illustration of The Concept For A One Dimensional Square Well
The one dimensional infinite square well of length L is a model for a one dimensional box. It is a standard model-system in quantum mechanics for which the solution for a single particle is well known. The levels are labeled by a single quantum number n and the energies are given by
Suppose now that instead of one particle in this box we have N particles in the box and that these particles are fermions with spin 1/2. Then not more than two particles can have the same energy, i.e., two particles can have the energy of, two other particles can have energy and so forth. The reason that two particles can have the same energy is that a particle can have a spin of 1/2 (spin up) or a spin of -1/2 (spin down), leading to two states for each energy level. In the configuration for which the total energy is lowest (the ground state), all the energy levels up to n=N/2 are occupied and all the higher levels are empty. The Fermi energy is therefore
Read more about this topic: Fermi Energy
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