Day 340: Hermitian and Unitary Operators — The Pillars of Quantum Mechanics

Learning Objectives

• •Define and compute the adjoint (Hermitian conjugate) of operators
• •Identify Hermitian operators and prove their eigenvalues are real
• •Prove that eigenvectors of Hermitian operators with distinct eigenvalues are orthogonal
• •Define unitary operators and verify they preserve inner products
• •Show that eigenvalues of unitary operators have unit modulus
• •Connect Hermitian operators to observables and unitary operators to quantum evolution

Today's Schedule (7 hours)