Student understanding of potential, wavefunctions and the Jacobian in hydrogen in graduate-level quantum mechanics Documents

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Student understanding of potential and wavefunctions in hydrogen in graduate-level quantum mechanics 

written by Chris D. Porter, Abigail M. Bogdan, and Andrew F. Heckler

This study examined student difficulties related to the potential in the hydrogen atom, and the corresponding ground state, with special attention paid to the role of the Jacobian. The study focused on a population of graduate students at The Ohio State University, and their ability to (1) sketch the approximate potential and radial part of the ground state wavefunction in hydrogen, and (2) their ability to relate this prerequisite knowledge to another relevant quantity: the Bohr radius. Student responses to a sequence of three questions were obtained at the beginning and end of the students' final semester of graduate quantum mechanics. Several prevalent difficulties were identified that persisted to the end of the course, including an inability to sketch the above-mentioned basic features of hydrogen, and a lack of understanding of the Bohr radius.

Last Modified November 30, 2016

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