Day 348: Position and Momentum Operators

Learning Objectives

• •Define the position operator $\hat{x}$ and understand its action on wave functions
• •Derive the momentum operator $\hat{p} = -i\hbar\frac{d}{dx}$ in position representation
• •Solve eigenvalue equations for position and momentum operators
• •Understand the relationship $\langle x|\psi\rangle = \psi(x)$
• •Work with both position and momentum representations
• •Verify the canonical commutation relation $[\hat{x}, \hat{p}] = i\hbar$

Today's Schedule (7 hours)