A new type of solution of the Schr\"odinger equation on a self-similar fractal potential

Scattering a quantum particle by a self-similar fractal potential on a Cantor set is investigated. We present a new type of solution of the functional equation for the transfer matrix of this potential, which was derived earlier from the Schr\"odinger equation.Comment: Latex, 4 pages, 7 eps-figures; the old figures are renewed and new ones are adde

Stationary states of an electron in periodic structures in a constant uniform electrical field

On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is developed. These solutions are shown to be current-carrying. It is also shown that the electron spectrum for infinite structures is continuous, and the corresponding wave functions do not satisfy the symmetry condition of the problem.Comment: 10 pages (Latex), no figures, in the revised variant some mistakes in the English text are corrected and also the first two paragraphs in the Conclusion are refined (Siberian physical-technical institute at the Tomsk state university, Tomsk, Russia