On the problem of an electron scattering in an arbitrary one-dimensional potential field

TL;DR

This paper derives recurrent formulas and differential equations to analyze electron scattering in one-dimensional arbitrary potential fields, enhancing understanding of quantum transmission and reflection phenomena.

Contribution

It introduces new recurrent representations and differential equations for scattering amplitudes in one-dimensional potentials, advancing theoretical methods in quantum scattering analysis.

Findings

Recurrent representations for transmission and reflection amplitudes derived.

Linear differential equations for scattering amplitudes established.

Applicable to arbitrary one-dimensional potentials.

Abstract

Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.