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Hermite polynomials and the quantum harmonic oscillator

📝 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   ~ Director and writer: BM Producer and designer: MC