Professor M does Science | 3D isotropic quantum harmonic oscillator: eigenvalues and eigenstates @ProfessorMdoesScience | Uploaded September 2022 | Updated October 2024, 2 hours ago.
📝 Problems+solutions:
- Quantum harmonic oscillator I: professorm.learnworlds.com/course/quantum-harmonic-oscillator-i
- Quantum harmonic oscillator II: professorm.learnworlds.com/course/quantum-harmonic-oscillator-ii

💻 Book a 1:1 session: docs.google.com/forms/d/e/1FAIpQLScUL187erItvC7GPnNU2pelsueyVFr94nRq2A5Eq2aVRdGiIQ/viewform?pli=1

📚 The 3D isotropic quantum harmonic oscillator can be described using a Hamiltonian of a central potential. In this video, we explicitly build the first few eigenvalues and eigenstates of this system. The eigenstates are written in terms of spherical harmonics because they are also eigenstates of orbital angular momentum.

0:00 Intro
1:34 3D isotropic quantum harmonic oscillator as a central potential
5:35 Recap of the mathematical solution of the eigenvalue equation
11:46 Ground state
19:58 First excited state
27:22 Second excited state
30:21 Wrap-up

⏮️ BACKGROUND
1D quantum harmonic oscillator: youtu.be/OdizRUe84bg
3D quantum harmonic oscillator in Cartesian coordinates: youtu.be/cZTnmlJfHdg
3D quantum harmonic oscillator in spherical coordinates: youtu.be/jOQThICjLlw
Central potentials: youtu.be/Y73ctxnP9gQ
Radial equation of central potentials: youtu.be/MsZP7yxpeFg
Orbital angular momentum: youtu.be/EyGJ3JE9CgE
Spherical harmonics: youtu.be/5PMqf3Hj-Aw

⏭️ WHAT NEXT?
Hydrogen atom: youtube.com/playlist?list=PL8W2boV7eVfnJbLf-p3-_7d51tskA0-Sa

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Director and writer: BM
Producer and designer: MC