Interactive Learning Platform on GitHub for Quantum Two-Body Bound States in Two Dimensions

We present the development of an innovative educational website, hosted on GitHub, designed to enhance understanding of quantum few-body systems in two-dimensional semiconductor materials through a blend of theoretical insights and practical, hands-on training. This resource is primarily aimed at training undergraduate students who possess introductory knowledge of quantum physics and are keen to explore computational approaches. The theoretical component of the website includes an introduction to quantum mechanics, a detailed exploration of the Schrödinger equation, and its application to quantum two-body bound states. It delves into the Lippmann-Schwinger equation both in momentum and configuration spaces, accompanied by relevant case studies such as the hydrogen atom, deuteron, and exciton, all within a two-dimensional framework. Complementing the theoretical discourse, the website offers interactive Python Jupyter Notebooks for hands-on training. This includes basic programming in Python, numerical solutions of integral equations using Gauss-Legendre quadrature, and practical implementations of the Lippmann-Schwinger equation in two-dimensional spaces. Detailed case studies allow users to apply these methods to analyze a hydrogen atom using the Coulomb potential, a deuteron using the Malfliet-Tjon potential, and an exciton using the Rytova-Keldysh potential. This interactive platform is accessible for public use on GitHub [https://csu-physics.github.io/] and serves as a valuable tool for students to bridge the gap between theoretical quantum mechanics and practical computational applications. By providing this resource, we aim to foster a deeper understanding of quantum behaviors in semiconductor materials through direct engagement and experimentation.