Lambert W Lines and Finite Square Well Sensors

TL;DR

This paper introduces a geometric method to analyze the sensitivity of finite quantum square well systems, providing visualizations and identifying conditions for heightened sensitivity to well parameters.

Contribution

It presents a novel geometric approach to determine bound state energies and explores the system's sensitivity to parameter changes with 3-D visualizations.

Findings

Identification of specific well strengths with high sensitivity

Development of a geometric mapping method for energy determination

Visualization of solution space in three dimensions

Abstract

The bound state energies of a 1-dimensional finite quantum square well (FSW) can be determined using a geometric method, involving a smooth mapping between two copies of the complex plane. The method allows one to identify particular strengths of the FSW at which the system can become unusually sensitive to changes in the well depth or geometry. In the present paper we explore that sensitivity, and exhibit a 3-D visualization of the solutions.