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

Authors

  • Lou Aidan M. De Jesus ⋅ PH Department of Physical Sciences, Polytechnic University of the Philippines
  • Rhenish C. Simon ⋅ PH Physics Department, De La Salle University, Manila

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.

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Issue

Article ID

SPP-2023-PC-06

Section

Poster Session C (Mathematical Physics, Optics, and Interdisciplinary Topics)

Published

2023-07-02

How to Cite

[1]
LAM De Jesus and RC Simon, Transfer matrix method to solve for bound state energies of a one-dimensional quantum well system, Proceedings of the Samahang Pisika ng Pilipinas 41, SPP-2023-PC-06 (2023). URL: https://proceedings.spp-online.org/article/view/SPP-2023-PC-06.