Undergraduate students’ visualization of quantum mechanical eigenstates and the role of boundary conditions

Abstract

Quantum mechanics (QM) is one of the core subject areas in the undergraduate physics curriculum and it is usually taught within an abstract framework. Visualization of concepts, such as energy eigenfunctions and their spatial dependence probability density, helps students to gain a deeper and more comprehensive understanding of QM. The role played by ‘boundary conditions’ in a given quantum system primarily governs energy eigenvalues as well as eigenfunctions. Therefore, visualization of the impact of boundary conditions on eigenvalues and eigenfunctions are of immense significance in building a coherent cognitive structure. In this study, we attempt to explore the challenges faced by undergraduate students in visualizing the eigenfunctions when the potential distribution is well defined. The research was carried out within a qualitative framework, which involved interaction with a group of undergraduate students and critical analysis of the responses from a constructivist viewpoint. The outcomes pointed towards prevalent alternate conceptions in the understanding of eigenfunctions. Specifically, the results showed the difficulties students face in associating eigenfunctions with prescribed boundary conditions for a potential distribution. The qualitative method allows us to ascertain the exact bottleneck which obstructs the creation of a coherent model and, subsequently, provides a route to address such issues.