mes 3Speak Podcast

Spherical Harmonics – Solutions to the Angular Laplacian

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https://3speak.tv/watch?v=mes/65445edf
In this video, I go over the actual spherical harmonics equations, which exclude the radial terms from the solid spherical harmonics I had derived earlier. The spherical harmonics can be combined into one function that contains all of the angular terms, thus essentially treating the sphere's radius as a constant. I also show how the spherical harmonics can be considered the solution of a modified Laplace equation, and hence a modified Laplace operator termed the angular Laplacian.

#math #sphericalharmonics #calculus #quantumphysics #laplace

Timestamps:

  • Spherical harmonics excludes the radial term and only has the angular terms – 0:00
  • Combine the radial terms into a function Y – 1:02
  • Y is considered the solution to the angular Laplacian – 2:44
  • Angular Laplacian excludes the radial terms – 4:33
  • Factor out the Y term from the radial term – 6:47
  • Choose separation constants just as with solid spherical harmonics – 7:28
  • Obtain the typical equation whose solution Y is the spherical harmonics – 8:56
  • Equation for Y, defined earlier – 10:13

    • Notes and playlists:

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    • Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FHh2kZzebadnPFwO6Yi5qu .

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      mes 3Speak PodcastBy Math Easy Solutions