Day 248: Spectral Theorem for Bounded Self-Adjoint Operators

Learning Objectives

• •**Define** spectral measures and projection-valued measures (PVM)
• •**State and understand** the spectral theorem for bounded self-adjoint operators
• •**Construct** the spectral family (resolution of the identity) for an operator
• •**Interpret** the spectral integral $A = \int \lambda \, dE_\lambda$
• •**Connect** spectral projections to quantum measurement collapse
• •**Apply** the spectral theorem to compute operator properties

Today's Schedule (7 hours)