Separation of Variables in Spherical Coordinates Lecture (30 minutes)

Central Forces Notes Section 33 (Appendix B) and 16

  • Adjust this lecture based on how much experience your students already have with Separation of Variables. We find it helpful if the several courses which use the technique of Separation of Variables all use the same steps to describe it. We wrote Appendix B to be a generic handout which can be used in these multiple settings.
  • Students have a tendency to just chop the equation up into several pieces without regard to whether or not each piece contains only one variable. Because factors of $r$ and $\sin\theta$ float around everywhere, this example is a good one in which to emphasize that one has to do enough algebra to isolate a single variable. Highlight the magic of the argument that allows each side of the equation to be set equal to a constant.
  • Prior to this, students may not have used the notation $R(r)$ where R represents the function of the variable r. We find that it is useful to be very explicit about this to help avoid student confusion in the extended calculations that follow. Some students may believe that $R(r)$ means $R$ multiplied by $r$.

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