Theory of finite periodic systems: The eigenfunctions symmetries

Abstract

Using the analytical expressions for the genuine eigenfunctions ${\phi }_{\mu \nu }(z)$ 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 $\nu$.

10 pages, 14 figures

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