Hermite polynomials and the quantum harmonic oscillator

Опубликовано: 26 Июнь 2026
на канале: Professor M does Science

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

📚 The eigenfunctions of the quantum harmonic oscillator can be written as a product of a Hermite polynomial and a Gaussian. In this video, we first introduce some of the mathematical properties of Hermite polynomials, and we then prove their relation to the eigenstates of the quantum harmonic oscillator.

⏮️ BACKGROUND
Harmonic oscillator:    • The quantum harmonic oscillator
Ladder operators:    • Ladder and number operators of the quantum...
Eigenvalues of the quantum harmonic oscillator:    • Eigenvalues of the quantum harmonic oscill...
Eigenstates of the quantum harmonic oscillator:    • Eigenstates of the quantum harmonic oscill...
Translation operator:    • The translation operator in quantum mechanics

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Director and writer: BM
Producer and designer: MC