Eigenvalues for systems in the canonical ensemble

Consider an ensemble of ? identical systems part of the canonical ensemble each with same volume and composition at thermal equilibrium. Let $ψ_j (vec{r_j}, t)$ denote the (normalized) wavefunction characterizing the physical state in which the kth system of the ensemble happens to be at time $t$; naturally, k = 1, 2, …,N. At a given instant the state of a system in the ensemble should be given by the Schrödinger equation

$ĤPsi_j = E_jPsi_j    j = 1, 2,3, …$

now the manual says that each $E_j$ depends on the volume ($V$) and composition $N$ and it writes $E_j(N,V)$ to make it more clear. Since every replica of the ensemble has the same volume and composition shouldn’t be all the $E_j$s degenerate? or I’m assuming somenthing wrong?