On Eigenvalues and Eigenfunctions Absent in the Actual Solid State Theory

Pedro Pereyra

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arXiv · cond-mat/0009064

On Eigenvalues and Eigenfunctions Absent in the Actual Solid State Theory

Pedro Pereyra

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Abstract

In this letter new, closed and compact analytic expressions for the evaluation of resonant energies, resonant bound-states, eigenvalues and eigenfunctions for both scattering and bounded $n$-cell systems are reported. It is shown that for (scattering and bounded) 1-D systems the eigenfunctions $Ψ_{μ,ν}(z)$ are simple and well defined functions of the Chebyshev polynomials of the second kind $U_{n}$, and the energy eigenvalues $E_{μ,ν}$ (in the $μ$-th band) are determined by the zeros of these polynomials. New insights on the energy gap and the localization effect induced by phase coherence are shown.

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Pedro Pereyra. 2000-09-05. On Eigenvalues and Eigenfunctions Absent in the Actual Solid State Theory. https://arxiv.org/abs/cond-mat/0009064

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