Quantum transmission for embedded, locally periodic potentials -- amplitude-phase approaches

TL;DR

This paper develops amplitude-phase methods to analyze quantum particle transmission through locally periodic potentials, deriving conditions for total transmission peaks and exploring band modifications and fusion phenomena.

Contribution

It introduces amplitude-phase approaches, including Floquet/Bloch periodic functions, to identify energies of total transmission in locally periodic quantum systems.

Findings

Derived closed-form conditions for transmission peaks.

Defined Floquet/Bloch energy band types affecting transmission.

Discussed band modifications and fusion phenomena.

Abstract

Quantum particle transmission through locally periodic potentials surrounded by symmetric exterior potentials is analyzed. Closed-form conditions for locating energy peaks of total transmission are derived. Floquet/Bloch energy band types are defined and found to affect the number of peaks in transmission bands. Modifications of band types and a band fusion phenomenon are discussed. The theoretical approaches suggested consist of several ways to express a Schr\"{o}dinger wave as an amplitude function multiplying a harmonic function of a phase function. In particular, an approach containing a Floquet/Bloch periodic amplitude function and a corresponding phase function is described for the locally periodic region, allowing a way to specify quantum numbers for energies of total transmission.