The spherical harmonics

📚 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 🐦 Follow me on Twitter:   / profmscience   ⏮️ BACKGROUND Orbital angular momentum:    • Orbital angular momentum in quantum mechanics   Orbital angular momentum eigenvalues:    • Orbital angular momentum eigenvalues   Orbital angular momentum eigenfunctions:    • Orbital angular momentum eigenfunctions   ⏭️ WHAT NEXT? The 3D quantum harmonic oscillator eigenfunctions: [COMING SOON] The hydrogen atom eigenfunctions: [COMING SOON] 👩‍💻 GITHUB Plot the spherical harmonics yourself: https://nbviewer.org/github/profmscie... ~ Director and writer: BM Producer and designer: MC