Spherical Harmonics – Solutions to the Angular Laplacian

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: Hive: Summary: https://inleo.io/threads/view/mes/re-leothreads-gahhcp2z Notes: https://peakd.com/hive-128780/@mes/220d6572 Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FHh2kZzebadnPFwO6Yi5qu . Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: [email protected] Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps