Desarrollo de un recurso educativo computacional para la enseñanza del método variacional en mecánica cuántica

Abstract

This work presents the development of an educational computational resource in Python, designed for the study of three quantum systems that produce electro- nic confinement—a phenomenon that leads to the discretization of energy levels. Using the variational method, implemented from a multiparametric approach, the ground state energies are calculated, and the method is extended, both theoreti- cally and practically, to the analysis of excited states. The result is a solid theoreti- cal framework for this extension, along with an educational software package that includes a graphical user interface (GUI), as well as an installer and uninstaller for GNU/Linux systems. The program guides users sequentially through the calculation of expected energies, gradient descent-based minimization, and the visualization of wavefunctions and probability densities, thus constituting an innovative, practical, and intuitive resource for teaching quantum mechanics. The software is available at the following repository: https://github.com/fisinforgh/SEQVS.git.