Eigenstates of the quantum harmonic oscillator

What do the energy eigenstates of the quantum harmonic oscillator look like? 📝 Problems+solutions: Quantum harmonic oscillator I: https://professorm.learnworlds.com/co... Quantum harmonic oscillator II: https://professorm.learnworlds.com/co... More learning material: https://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:   / profmscience   ⏮️ BACKGROUND Harmonic oscillator:    • The quantum harmonic oscillator   Ladder and number operators:    • Ladder and number operators of the quantum...   Eigenvalues of the quantum harmonic oscillator:    • Eigenvalues of the quantum harmonic oscill...   Harmonic oscillator eigenvalues:    • Eigenvalues of the quantum harmonic oscill...   The parity operator:    • The parity operator in quantum mechanics   Even and odd operators:    • Even and odd operators in quantum mechanics   Wave functions:    • Wave functions in quantum mechanics   Position and momentum:    • Position and momentum operators acting on ...   ⏭️ WHAT NEXT? Hermite polynomials:    • Hermite polynomials and the quantum harmon...   Coherent states:    • Coherent states in quantum mechanics   ~ Director and writer: BM Producer and designer: MC