In this video, I graph out the real spherical harmonics using the amazing Desmos graphing calculator via a project someone made. I do a quick breakdown of the formulas they used, noting the added normalization constants, and how it matches up with our derived formulas from solving Laplace's equation in spherical coordinates. I also show what effects tinkering with the principal, orbital angular momentum, and magnetic quantum numbers has on the resulting 3D figures!
#math #sphericalharmonics #calculus #quantumphysics #desmos
Timestamps
- Real Spherical Harmonics in Desmos graphing calculator: https://www.desmos.com/calculator/nsfrepxacm – 0:00
- Radial distance is stretched proportionally to the magnitude of its value on the sphere – 3:53
- Principle magnetic number sets the maximum orbital angular momentum, which then sets the +/- limits of the magnetic quantum number – 5:30
- Graphs of real spherical harmonics for various quantum numbers – 7:14
- Graphing in Desmos – 8:19
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