Day 249: Functional Calculus

Learning Objectives

• •**Construct** the continuous functional calculus for self-adjoint operators
• •**Extend** to the Borel functional calculus for measurable functions
• •**Compute** operator functions like $e^{iAt}$, $\sqrt{A}$, $|A|$, $A^+$, $A^-$
• •**Apply** the spectral mapping theorem to determine spectra of $f(A)$
• •**Connect** functional calculus to quantum mechanical time evolution
• •**Implement** numerical methods for computing functions of matrices

Today's Schedule (7 hours)