Day 414: Rotation Operators

Learning Objectives

• •**Describe classical rotation matrices** as elements of the special orthogonal group SO(3)
• •**Derive the quantum rotation operator** $$\hat{R}(\hat{n},\theta) = e^{-i\theta\hat{n}\cdot\hat{\mathbf{J}}/\hbar}$$
• •**Apply infinitesimal rotations** to identify angular momentum as the generator
• •**Demonstrate non-commutativity** of finite rotations (non-Abelian structure)
• •**Connect rotation operators to SU(2)** and understand the double cover relationship
• •**Implement rotation operators** computationally for various angular momentum values

Today's Schedule (7 hours)