From the previous post "Fermi–Dirac Statistics But Twisted", by considering the distribution of \(\psi\) as \(x_{z}\) varies,
\(\int_{all\,x_z}{D(x_z)}\,d\,x_z=\psi\)
where \(D(x_z)\) is the distribution of \(\psi\) along \(x_z\). Differentiating wrt \(x_z\)
\(\cfrac{\partial\,\psi}{\partial\,x_z}=D(x_z)\)
In which case \(x_z\) determines the energy density \(\psi\) completely. Pauli exclusion principle does not matter at all. It is, in the first place, odd to consider the exclusion principle and degenerate states, where many states can have the same energy, at the same time.
\(\psi\) is not discrete. \(\psi(x_z)\) is continuous for \(0\le x_z\lt x_{z\,max}\).
