65 research outputs found
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
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