Day 394: Commutation Relations of Angular Momentum

Learning Objectives

• •**Derive** $[\hat{L}_x, \hat{L}_y] = i\hbar\hat{L}_z$ from the canonical commutation relations
• •**Express** the general commutation relation using the Levi-Civita symbol
• •**Prove** that $\hat{L}^2$ commutes with all angular momentum components
• •**Explain** why we can only have simultaneous eigenstates of $\hat{L}^2$ and one component
• •**Apply** the angular momentum uncertainty relations
• •**Construct** matrix representations of angular momentum operators

Today's Schedule (7 hours)