Transfer matrix method to solve for bound state energies of a one-dimensional quantum well system

Abstract

Introductory quantum mechanics courses focus heavily on ideal models of quantum wells and not as much on finite cases more applicable in realistic semiconductor structures. The transfer matrix method (TMM) is a well known method for solving arbitrary finite well structures. This paper aims to re-examine the TMM as a pedagogy for analyzing quantum mechanical systems. We used the TMM to create a Python script that simulates arbitrary piecewise constant finite wells and calculates their eigenenergies. We then compared the simulated eigenenergies to their known analytic solutions. This contribution may serve as a guide to equip students and educators with a simple algorithm for analysis and visualization of quantum well systems.