Quantum Superlattices, Wannier Stark Ladders and the 'Resonance' technique

TL;DR

This paper introduces a novel application of the Lossless Transmission Line Model (LTL) to solve the Schrödinger equation for solid state systems, demonstrating its flexibility and effectiveness for arbitrary potentials.

Contribution

The paper develops a transformation theory mapping the wave equation to LTL and extends it with a Wannier-Stark term, applying it to periodic lattices in solid state physics.

Findings

Successfully applied LTL to solid state lattice problems

Extended the model with Wannier-Stark terms

Showed advantages for arbitrary potentials

Abstract

We present a new method for solving the Schrodinger equation using the Lossless Transmission Line Model (LTL). The LTL model although extensively used in fiber optics and optical fiber design, it has not yet found application in solid state problems. We develop the transformation theory mapping the wave equation to LTL and we apply the model to the case of a solid state periodic lattice. We extend the theory with an additional Wannier-Stark term and we show with results the flexibility and the strength of the technique. The advantages of the method for arbitrary potentials are also stressed.