On quantum bound states in equiperiodic multi-well potentials I: $-$ Locally periodic potential sequences and Floquet/Bloch bands

TL;DR

This paper investigates quantum bound states in connected, locally periodic multi-well potentials, revealing how Floquet/Bloch bands influence the energy level structure and create quantum-mechanical forbidden regions despite classical allowance.

Contribution

It introduces the analysis of Floquet/Bloch band structures in connected multi-well potentials with different depths, highlighting their role in quantum level formation and forbidden regions.

Findings

Energy levels lie within band regions despite classical allowance.

Band gaps create quantum-mechanical forbidden zones.

Floquet/Bloch bands determine the quantum level structure.

Abstract

Two connected equiperiodic one-dimensional multi-well potentials of different well depths are studied. Floquet/Bloch energy bands for respective multi-well potential are found to be relevant for understanding level structures. Althoug energies are classically allowed in both multi-well potentials, a band gap of one multi-well potential makes this potential quantum-mechanically 'forbidden'. All energy levels are located in the union of the band regions.