Exact electron states in 1D (quasi-) periodic arrays of delta-potentials

TL;DR

This paper derives exact one-electron eigenstates in finite 1D periodic and quasiperiodic delta potential arrays, analyzing their properties, boundary conditions, and scattering behavior, with implications for understanding band structures in quasiperiodic systems.

Contribution

It provides a method to compute exact eigenstates in finite 1D delta potential arrays and relates boundary conditions to transfer matrices, advancing understanding of quasiperiodic electronic states.

Findings

Exact eigenstates for finite 1D delta potential arrays are derived.

The relationship between Bloch and bound states via transfer matrices is established.

Scattering matrices and energy dependence are analyzed.

Abstract

Exact one-electron eigenstates in finite parts of 1D periodic and Fibonacci chains of attractive and repulsive delta potentials are computed and analyzed. Bloch and bound state boundary conditions are related in terms of transfer matrices. Scenarios of positive and negative energy are distinguished. The dependence on the potential strength parameter is analyzed. The scattering matrix is computed. Implications for the interpretation of band germs in quasiperiodic chains are discussed.