Journal of Physical Studies 25(4), Article 4001 [9 pages] (2021)
DOI: https://doi.org/10.30970/jps.25.4001

REFORMULATION OF TRANSMISSION AND REFLECTION PROBLEMS IN TERMS OF QUANTUM WAVE IMPEDANCE FUNCTION

O. I. Hryhorchak 

Professor Ivan Vakarchuk Department for Theoretical Physics, Ivan Franko National University of Lviv,
12, Drahomanov St., Lviv, UA–79005, Ukraine
e-mail: Orest.Hryhorchak@lnu.edu.ua

Received 17 September 2021; in final form 08 November 2021; accepted 07 December 2021; published online 29 December 2021

On the basis of 1D Schrödinger equation, a non-linear first-order differential equation (Riccati type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for the case of a single rectangular barrier. Both the scattering and the bound states problems were reformulated in terms of quantum wave impedance. The application of the method for solving these problems was considered. The expressions for the reflection and transmission coefficients were found on the basis of the quantum wave impedance approach.

Key words: Schrödinger equation, quantum mechanical wave impedance, scattering, tunneling.

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