Professor M does Science | Eigenstates of the quantum harmonic oscillator @ProfessorMdoesScience | Uploaded April 2021 | Updated October 2024, 3 hours ago.
What do the energy eigenstates of the quantum harmonic oscillator look like?

📝 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
- More learning material: professorm.learnworlds.com

📚 The eigenfunctions of the quantum harmonic oscillator are famously given by the product of a polynomial and a Gaussian. In this video, we derive their mathematical form and visualize a few representative states.

🐦 Follow me on Twitter: twitter.com/ProfMScience

⏮️ BACKGROUND
Harmonic oscillator: youtu.be/OdizRUe84bg
Ladder and number operators: youtu.be/Kb9twGd25P0
Eigenvalues of the quantum harmonic oscillator: youtu.be/GkUXscdLQQ0
Harmonic oscillator eigenvalues: youtu.be/GkUXscdLQQ0
The parity operator: youtu.be/OsvXeTEQxyg
Even and odd operators: youtu.be/o8l6Yz9EHps
Wave functions: youtu.be/2lr3aA4vaBs
Position and momentum: youtu.be/Yw2YrTLSq5U

⏭️ WHAT NEXT?
Hermite polynomials: youtu.be/p22UrUv9QdM
Coherent states: youtu.be/x0wk98uMyys

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Director and writer: BM
Producer and designer: MC