Methodology Of Teaching The Topic “Spherically Symmetric Potential Well” Using Digital Technologies In The Course Of Quantum Mechanics

Abstract

This article explores the methodology of teaching the topic “Spherically Symmetric Potential Well” within quantum mechanics courses at higher education institutions by integrating digital technologies. The spherically symmetric potential well is a fundamental concept in quantum mechanics, describing a system where the potential energy depends solely on the radial distance from the center. The complexity of the wave functions and the solutions to the Schrödinger equation for such systems makes the topic challenging for students. To enhance understanding, the study incorporates modern pedagogical tools, including mathematical modeling, virtual laboratories, and simulation software. The paper describes the use of platforms like MATLAB, Mathematica, and Wolfram Alpha to visualize wave functions and probability densities, while PhET simulations and Quantum Experience allow interactive exploration of quantum states. A custom-designed program developed for the study enables students to graph normalized wave functions, identify extremum points, calculate probabilities in various spherical regions, and examine energy levels as a function of quantum numbers. Practical applications of the software are demonstrated through problems that require both analytical and numerical solutions. The methodology encourages students to integrate mathematical analysis with graphical representations to solve complex quantum problems. The article concludes that the inclusion of digital technologies not only simplifies the teaching of abstract quantum mechanical concepts but also increases student engagement, retention, and competence in applying theoretical principles to real-world scenarios.