ERS approximation for solving Schr\"odinger's equation and applications

TL;DR

This paper reviews the ERS approximation method for solving Schrödinger's equation, demonstrating its improved accuracy over WKB, and explores its applications to bound states, quantum wires, and Anderson localization.

Contribution

It introduces a comprehensive review of the ERS approximation and its application to complex quantum systems, including disordered potentials.

Findings

ERS provides better accuracy than WKB for Schrödinger solutions.

Application to quantum wires illustrates ERS's effectiveness in disordered systems.

Discussion of ERS in the context of Anderson localization highlights its practical relevance.

Abstract

A new technique was recently developed to approximate the solution of the Schroedinger equation. This approximation (dubbed ERS) is shown to yield a better accuracy than the WKB-approximation. Here, we review the ERS approximation and its application to one and three-dimensional systems. In particular, we treat bound state solutions. We further focus on random potentials in a quantum wire and discuss the solution in the context of Anderson localization.