The three-dimensional isotropic and non-relativistic uniform Fermi gas case is known as the Fermi sphere.
A three-dimensional infinite square well, (i.e. a cubical box that has a side length L) has the potential energy
The states are now labelled by three quantum numbers n, n, and n. The single particle energies are
where n, n, n are positive integers. In this case, multiple states have the same energy (known as degenerate energy levels), for example .