Professor M does Science | The spherical harmonics @ProfessorMdoesScience | Uploaded October 2021 | Updated October 2024, 3 hours ago.
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📚 The spherical harmonics are the eigenstates of orbital angular momentum in quantum mechanics. As such, they feature in the wave functions of many quantum problems, including the 3D quantum harmonic oscillator and the hydrogen atom. In this video, we write down the mathematical form of the first few spherical harmonics, and we also visualize them with animated 3D graphics.

0:00 Intro
0:45 Definition of the spherical harmonics
3:09 How do we visualize spherical harmonics?
6:37 l=0 spherical harmonic
8:14 l=1 spherical harmonics
17:16 l=2 spherical harmonics
18:53 l=3 spherical harmonics
19:50 An alternative view of the spherical harmonics
23:01 Wrap-up

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⏮️ BACKGROUND
Orbital angular momentum: youtu.be/EyGJ3JE9CgE
Orbital angular momentum eigenvalues: youtu.be/5h5mbL5rco0
Orbital angular momentum eigenfunctions: youtu.be/Gk2XNmIHVwo

⏭️ WHAT NEXT?
The 3D quantum harmonic oscillator eigenfunctions: [COMING SOON]
The hydrogen atom eigenfunctions: [COMING SOON]

👩‍💻 GITHUB
Plot the spherical harmonics yourself: nbviewer.org/github/profmscience/spherical-harmonics/blob/main/spherical-harmonics-for-github.ipynb

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Director and writer: BM
Producer and designer: MC