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Stationary motion of a quantum particle in an arbitrary one-dimensional potential

  • Lattice Dynamics and Phase Transitions
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Abstract

A consistent approach to the description of a stationary motion of a quantum particle in an arbitrary one-dimensional potential has been developed. It has been proved that the wave function of an infinite motion can be expressed accurate to up two arbitrary constants with the use of one particular solution to the system of first-order linear differential equations. It has been shown that many well-known methods, such as the integral equation method, the transfer matrix method, the embedding method, and the method of combination of scattering parameters, are based on a general property of the solutions to the Schrödinger equation. Within the proposed approach, the relation between these methods becomes more transparent and their description can be well within a unified context.

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Authors and Affiliations

  1. State Engineering University of Armenia, ul. Teryan 105, Yerevan, 375009, Armenia

    A. Zh. Khachatrian

  2. Yerevan State University, ul. Aleks Manukyan 1, Yerevan, 375049, Armenia

    D. M. Sedrakian & V. A. Khoetsyan

Authors
  1. A. Zh. Khachatrian
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  2. D. M. Sedrakian
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  3. V. A. Khoetsyan
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Corresponding author

Correspondence to A. Zh. Khachatrian.

Additional information

Original Russian Text © A.Zh. Khachatrian, D.M. Sedrakian, V.A. Khoetsyan, 2010, published in Fizika Tverdogo Tela, 2010, Vol. 52, No. 7, pp. 1404–1411.

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Khachatrian, A.Z., Sedrakian, D.M. & Khoetsyan, V.A. Stationary motion of a quantum particle in an arbitrary one-dimensional potential. Phys. Solid State 52, 1506–1514 (2010). https://doi.org/10.1134/S1063783410070279

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  • DOI: https://doi.org/10.1134/S1063783410070279

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