Day 242: Self-Adjoint and Unitary Operators

Learning Objectives

• •**Define** self-adjoint, unitary, and normal operators
• •**Prove** that self-adjoint operators have real spectrum
• •**Prove** that unitary operators preserve inner products and norms
• •**Verify** operator classification for specific examples
• •**Explain** why observables must be self-adjoint and symmetries must be unitary
• •**Connect** normal operators to the spectral theorem

Today's Schedule (7 hours)