Professor M does Science | The 3D quantum harmonic oscillator @ProfessorMdoesScience | Uploaded September 2021 | 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 harmonic oscillator is one of the most important systems in quantum mechanics, used to describe a plethora of phenomena, from atomic vibrations (phonons) to light. In this video, we use the properties of tensor product state spaces to solve the 3-dimensional quantum harmonic oscillator from our knowledge of the solutions of the 1-dimensional counterpart.

0:00 Intro
1:07 3D quantum harmonic oscillator Hamiltonian
6:39 Solving the eigenvalue equation
9:02 Eigenvalues
9:58 Eigenstates
15:43 Eigenfunctions
19:22 Wrap-up

⏮️ BACKGROUND
1D quantum harmonic oscillator: youtu.be/OdizRUe84bg
Ladder operators: youtu.be/Kb9twGd25P0
Eigenvalues of the quantum harmonic oscillator: youtu.be/GkUXscdLQQ0
Eigenstates of the quantum harmonic oscillator: youtu.be/0o-LoJRtxDc
Hermite polynomials: youtu.be/p22UrUv9QdM
Coherent quantum states: youtu.be/x0wk98uMyys
Tensor product state spaces: youtu.be/kz3206S2B6Q
Eigenvalues and eigenstates in tensor product spaces: youtu.be/T3ynwXrE0Xw

⏭️ WHAT NEXT?
Degeneracies of the isotropic quantum harmonic oscillator: youtu.be/K5YsxsHXGHc
The 3D quantum harmonic oscillator as a central potential: [COMING SOON]

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Director and writer: BM
Producer and designer: MC