Improving student understanding of a system of identical particles with a fixed total energy

Abstract

We discuss an investigation of student difficulties with whether a given total energy is possible for the system under given constraints, the possible outcomes of an energy measurement, and the probability of obtaining a particular energy if we randomly measured the energy of one particle and concepts involved in determining the number of distinct many-particle states in a system of noninteracting identical particles with a fixed total energy. The investigation was carried out in advanced quantum mechanics courses by administering free-response and multiple-choice questions and conducting individual interviews with students. We also discuss how the research was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT), which strives to help students develop a functional understanding of the relevant concepts for a system of non-interacting identical particles with a fixed total energy. We discuss the development and validation of the identical particles QuILT and its evaluation in the undergraduate and graduate courses that focused on these issues.