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Operators and Functions

Keywords: Oscillations & Waves, Quantum Mechanics, Operators, Middle Division, Eigenfunction, Eigenstate


Highlights of the activity

  1. This small group activity is designed to help upper-division undergraduate students transition between different representations of quantum mechanical operators and practice expanding functions as superpositions of eigenfunctions.
  2. Students investigate the differential forms of quantum mechanical operators and identify eigenfunctions and eigenvalues for each operators.
  3. The wrap-up discussion reinforces how eigenfunctions can be identified and highlight similarities/differences in the eigenfunctions for the momentum and energy operators.

Reasons to spend class time on the activity

Eigenstates and eigenvalues are central to modeling quantum phenomena. It is important for students to develop facility with the matrix and function forms of vector spaces and with identifying eigenstates and eigenvalues. We use this activity as a introduction to differential operators. Students are encouraged to make connections to their knowledge of eigenstates in the special case of 2-state systems (spin).


Instructor's Guide

Student Handouts



Authors: Janet Tate, Elizabeth Gire (activity page)
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