Day 382: QHO Wave Functions — Hermite Polynomials

Learning Objectives

• •Derive the ground state wave function from $\hat{a}|0\rangle = 0$
• •Understand the Hermite polynomial solutions and their properties
• •Write explicit wave functions $\psi_n(x)$ for arbitrary $n$
• •Prove orthonormality using wave function integrals
• •Visualize probability densities and classical turning points
• •Connect wave function nodes to quantum numbers

Today's Schedule (7 hours)