Three-dimensional neutron gas
Using the same approach as made with the two-dimensional electron gas with the single-particle kinetic energy defined as
$$
\frac{\hbar^2}{2m}\left(k_{n_x}^2+k_{n_y}^2k_{n_z}^2\right),
$$
and
$$
k_{n_i}=\frac{2\pi n_i}{L} \hspace{0.1cm} n_i = 0, \pm 1, \pm 2, \dots,
$$
we can set up a similar table and obtain (assuming identical particles one and including spin up and spin down solutions) for energies less than or equal to \( n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\le 3 \)