Investigating how Students Think About and Learn Quantum Physics: An Example from Tunneling

Much of physics education research (PER) has focused on introductory courses and topics, with less research done into how students learn physics in advanced courses. Members of The University of Maine Physics Education Research Laboratory (PERL) have begun studying how students in advanced physics courses reason about classical mechanics, thermal physics, and quantum physics. Here, we describe an investigation into how students reason about quantum mechanical tunneling, and detail how those findings informed a portion of a curriculum development project. Quantum mechanical tunneling is a standard topic discussed in most modern physics and quantum physics courses. Understanding tunneling is crucial to making sense of several topics in physics, including scanning tunneling microscopy and nuclear decay. To make sense of the standard presentation of tunneling, students must track total, potential, and kinetic energies. Additionally, they must distinguish between the ideas of energy, probability density, and the wave function. They need to understand the complex nature of the wave function, as well as understand what can and cannot be inferred from a solution to the time-independent Schrödinger equation. Our investigations into student understanding of these ideas consisted of a series of interviews, as well as a survey. Both centered around asking students to reason about energy, probability, and the wave function solutions for the standard square potential energy barrier scenario presented in most textbooks. We describe ideas that students seem to successfully learn following standard instruction, as well as common difficulties that remain. Additionally, we present multiple data points from a small population of physics majors over three years and describe how some of their reasoning about tunneling changed, while other portions seemed to remain unaffected by instruction. We used the results of these investigations to write tutorials on tunneling and applications of tunneling. The tutorials were part of a course on introductory quantum physics for non-science majors. In this course, most of the ideas were introduced in the small-group, student-centered tutorial-labs. We present evidence that this population can learn some basic ideas of quantum physics, and on certain tunneling questions perform as well or better than advanced undergraduate students