Professor M does Science | Orbital angular momentum eigenfunctions @ProfessorMdoesScience | Uploaded February 2021 | Updated October 2024, 1 hour ago.
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📚 The eigenvalues of orbital angular momentum are quantized. In this video, we construct the corresponding eigenfunctions, called spherical harmonics. The derivation of the eigenfunctions is conceptually simple, and it is covered in the first part of the video. The maths is somewhat involved but rather elegant, featuring interesting integrals and recurrence relations, and the second part of the video goes over these manipulations in detail for the more mathematically-minded amongst you.

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⏮️ BACKGROUND
General angular momentum: youtu.be/Bo5qoaLsBOE
Ladder operators: youtu.be/yGvfqRfw1BE
General angular momentum eigenvalues: youtu.be/t7x6vt6xkAI
Orbital angular momentum: youtu.be/EyGJ3JE9CgE
Orbital angular momentum eigenvalues: youtu.be/5h5mbL5rco0

⏭️ WHAT NEXT?
Spherical harmonics: youtu.be/5PMqf3Hj-Aw

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Director and writer: BM
Producer and designer: MC