Periodic almost-Schrodinger equation for quasicrystals

TL;DR

This paper introduces a novel method for calculating electronic structures in quasicrystals using a modified Schrödinger equation in higher-dimensional spaces, providing exact results efficiently.

Contribution

The paper presents a new approach that simplifies and improves the accuracy of electronic structure calculations in quasicrystals by leveraging higher-dimensional Schrödinger equations.

Findings

Successfully applied to 1D quasiperiodic Coulomb potential

Achieves exact results without costly approximations

Demonstrates efficiency and accuracy of the new method

Abstract

A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrodinger equation in spaces of dimensionality higher than physical space. It enables to get exact results for quasicrystals without expensive non-exact calculations. New method tested on one-dimensional quasiperiodic screened Coulomb potential.