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Expectation Values for a Particle on a Ring

Keywords: Central Forces, Quantum Mechanics, Eigenstates, Eigenvalues, Hermitian Operators, Quantum Measurements, Degeneracy, Expectation Values, Time Dependence, Small Group Activity


Highlights of the activity

  1. This small group activity is designed to help students work out expectation values for a quantum particle confined to a ring.
  2. Students work in small groups with eigenstates of a quantum particle confined to a ring and calculate the expectation value for angular momentum and energy as a function of time.
  3. The whole class wrap-up discussion includes group presentations, allowing students to witness a variety of techniques in computing expectation values, and opens up a general conversation about quantum measurement.

Reasons to spend class time on the activity

Students commonly attempt to determine the values resulting from a quantum experiment by allowing the operator corresponding to the observable of interest to act on the initial state. Expectation values are one of the few calculations where the operator actually acts on a state to change it, providing an opportunity to address this issue with students.


Instructor's Guide

Student Handouts



Authors: Corinne Manogue, Kerry Browne, Elizabeth Gire, Mary Bridget Kustusch, David McIntyre
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