POINT SPECTRUM OF SCHRODINGER OPERATOR FOR TWO CONNECTED SEMICRYSTALS WITH KRONIG-PENNEY POTENTIALS

Anastasiya Skorynina

2010 , VOLUME 10, NUMBER 6 ( NOVEMBER-DECEMBER )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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Vladimir O.
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POINT SPECTRUM OF SCHRODINGER OPERATOR FOR TWO CONNECTED SEMICRYSTALS WITH KRONIG-PENNEY POTENTIALS

A. Skorynina

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Abstract

Spectral problem for two connected one-dimensional semicrystals is considered in the framework of Kronig-
Penney model. Two variants of this connection are studied. The dispersion equations are obtained. The existence of bound states is shown. The dependence of the eigenvalues in the system parameters is described. The monodromy matrix technique is used.

Keywords: spectrum, one-dimensional Schrodinger operator, periodic potential, semicrystal

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