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

• URL: http://arxiv.org/abs/2005.11695v1
• Date: Sun, 24 May 2020 09:20:39 GMT
• Title: Quantum transmission for embedded, locally periodic potentials -- amplitude-phase approaches
• Authors: Karl-Erik Thylwe
• Abstract summary: Quantum particle transmission through locally periodic potentials surrounded by symmetric exterior potentials is analyzed. Floquet/Bloch energy band types are defined and found to affect the number of peaks in transmission bands.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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