Extension of Some Theorems on the Eigenvalue Spectra of One-Dimensional Systems To Linear Chains
Phys. Rev. A 6, 2478 – Published 1 December, 1972
DOI: https://doi.org/10.1103/PhysRevA.6.2478
Abstract
The possibility of extending theories of strictly one-dimensional systems to linear systems is examined. Shockley's theorem is proved for the former case and shown not to be valid for the latter. On the subject of localized states, it is shown that only a limited generalization is possible, but that this may be sufficient for calculations on real disordered polymer chains.