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Linear Combinations of Spherical Harmonics

Keywords: Quantum Mechanics, Spherical Harmonics, Computer Visualization

cfylmcombo.jpg

Highlights of the activity

  1. This computer visualization activity is designed to help upper division undergraduate students visualize linear combinations of spherical harmonics.
  2. Students use Maple worksheet or Mathematica notebook to visualize various representations of probability densities of linear combinations of spherical harmonics.
  3. The entire class wrap-up discussion addresses how to represent linear combinations of spherical harmonics in a variety of ways.

Reasons to spend class time on the activity

We find that many students have difficulty understanding the role of special functions in physics. The Maple worksheet provides different (equivalent) representations of probability densities computed from linear combinations of spherical harmonics. Being able to use all representations and understand their equivalence is a landmark on the students' path to becoming professional physicists.

Reflections

Instructor's Guide

Maple Worksheet

cfylmcombo.mw (Maple 13)

cfylmcombo.mws (Maple 11 Classic)

Mathematica Notebook

cfylmcombo.nb


Authors: Kerry Browne, Corinne Manogue
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