The Nature of the Electronic States in Disordered One-Dimensional Systems

摘要: We consider an electron moving in the field of a one-dimensional infinite chain identical potentials separated by regions zero potential, lengths s these being distributed according to probability density function p(8) . If we define reduced phase real solution wave equation as principal value arctan ( — ψ9/kψ ) and є i at point x immediately left th atomic it is shown for all bounded p(s) sufficiently high energies that are which depends on direction integration from specified homogeneous boundary condition. This result imply eigenfunctions such systems localized sense envelope decays average exponential manner either side some region. An analytical calculation random δ-functions gives decay nodes explicitly energies, numerical calculations liquid model presented. Further support theory provided computer 1000 randomly placed δ-functions.