Professor M does Science | Eigenvalues of the quantum harmonic oscillator @ProfessorMdoesScience | Uploaded March 2021 | Updated October 2024, 1 hour ago.
What are the possible energy eigenvalues of the quantum harmonic oscillator?

📝 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 harmonic oscillator is an iconic potential in both classical and quantum mechanics. In quantum mechanics, the energy is quantized: the eigenvalues can only take some special values. In this video, we derive the possible energy eigenvalues using an elegant approach first proposed by Paul Dirac that exploits the properties of the ladder operators.

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⏮️ BACKGROUND
Harmonic oscillator: youtu.be/OdizRUe84bg
Ladder operators: youtu.be/Kb9twGd25P0

⏭️ WHAT NEXT?
Eigenstates of the quantum harmonic oscillator: youtu.be/0o-LoJRtxDc


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Director and writer: BM
Producer and designer: MC