Using the analytical expressions for the genuine eigenfunctions
$\varphi_{\mu\nu}(z)$ and eigenvalues $E_{\mu,\nu}$, of open, bounded and
quasi-bounded finite periodic systems, we derive the eigenfunctions
space-inversion symmetry relations. The superlattice eigenfunctions symmetries,
closely related with the symmetries and zeros of the Chebyshev polynomials of
the second kind $U_n$, are fully written in terms of the number of unit cells
$n$, the subband index $\mu$ and the intra-subband index $\nu$.Comment: 10 pages, 14 figure