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Solutions of the Schrödinger equation in the case of a semiinfinite crystal

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Abstract

It is shown that bounded solutions of Bloch type with respect to the variablesx 1,x 2 for a Schrödinger equation in which the potential is periodic in the half-space {x 3≥0} and decreases exponentially asx 3→−∞ can be approximated by the solutions of the Schrödinger equation for a “thick film” when the number of its layers tends to infinity. Under certain conditions, this makes it possible to find the number of linearly independent solutions of such kind.

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Authors
  1. Yu. P. Chuburin
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Additional information

Physicotechnical Institute, Urals Scientific Center, Russian Academy of Sciences, Sverdlovsk. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 38–47, January, 1994.

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Chuburin, Y.P. Solutions of the Schrödinger equation in the case of a semiinfinite crystal. Theor Math Phys 98, 27–33 (1994). https://doi.org/10.1007/BF01015120

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  • DOI: https://doi.org/10.1007/BF01015120

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