written by Christof Keebaugh, Emily Marshman, and Chandralekha Singh

We discuss an investigation of student difficulties with determining the number of distinct many-particle stationary states for a system of non-interacting identical particles. Here we focus on a system in which there are a fixed number of available single-particle states and a fixed number of particles but the total energy of the system is not fixed. 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 find that upperlevel undergraduate and graduate students share many common difficulties related to these concepts. Many students struggled to determine the number of distinct many-particle stationary states and make connections between the number of distinct many-particle stationary states and the number of many-particle stationary state wavefunctions possible with the given constraints. Additionally, we found that many students had difficulty with mathematical sense-making in the context of quantum mechanics.

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Last Modified February 4, 2019

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