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Introduction to Bra-Ket Notation

Keywords: Middle-division, quantum mechanics, linear algebra, bra-ket notation


Highlights of the activity

  1. This small group activity is designed to introduce students to the basics of bra-ket notation.
  2. Students are given a handout that introduces them to the use of bra-ket notation and how it relates to other vector representations.
  3. The wrap-up discussion covers how to draw a 2-dimensional complex vector. Students struggle with this idea in QM since representing a 2D complex vector requires a 4D space. We reinforce the idea that complex vectors work just like real vectors as long as you remember to take the complex conjugate of elements of Bra's.

Reasons to spend class time on the activity

Learning how to use a new notation is problematic, so it is important to provide opportunities for students to explicitly connect the notation that they are learning to one(s) they are familiar with.


Instructor's Guide

Student Handouts



Authors: Corinne Manogue, Kerry Browne
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