Degeneracies of the 3D quantum harmonic oscillator

📝 Problems+solutions:
Quantum harmonic oscillator I: https://professorm.learnworlds.com/co...
Quantum harmonic oscillator II: https://professorm.learnworlds.com/co...

📚 The 3D quantum harmonic oscillator can be described as a simple combination of three 1D quantum harmonic oscillators along the three Cartesian directions. Despite this apparent simplicity, when the 3D oscillator is isotropic, the energy spectrum becomes highly degenerate. In this video, we explore these degeneracies by considering the different states that share the same energy, visualizing the associated eigenfunctions.

0:00 Intro
2:41 3D isotropic quantum harmonic oscillator
9:31 Ground state
11:56 First excited state
15:50 Second excited state
19:58 General case
22:53 Wrap-up

⏮️ BACKGROUND
1D quantum harmonic oscillator:    • The quantum harmonic oscillator  
Eigenvalues of the quantum harmonic oscillator:    • Eigenvalues of the quantum harmonic oscill...  
Eigenstates of the quantum harmonic oscillator:    • Eigenstates of the quantum harmonic oscill...  
3D quantum harmonic oscillator:    • The 3D quantum harmonic oscillator  

⏭️ WHAT NEXT?
The 3D quantum harmonic oscillator as a central potential: [COMING SOON]

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Director and writer: BM
Producer and designer: MC