Introduction -- Mathematical Introduction -- Free Particle Schroedinger Equation -- Free-Particle Wave Packets -- Schroedinger's Equation with Potential Energy: Introduction to Operators -- Postulates and Basic Elements of Quantum Mechanics: Properties of Operators -- Problems in 1-dimension: General Considerations, Infinite Well Potential, Piecewise Constant Potentials, and Delta Function Potentials -- Simple Harmonic Oscillator -- One Dimension -- Problems in 2 and 3-dimensions -- General Considerations -- Central Forces and Angular Momentum -- Spherically Symmetric Potentials -- Radial Equation -- Dirac Notation -- Spin -- Important Basics from Phys 453 -- Perturbation Theory -- Variational Approach -- WKB Approximation -- Scattering -- 1-D -- Scattering -- 3-D -- Symmetries and Transformations -- Rotations -- Examples -- Addition of Angular Momentum: Clebsch-Gordan Coefficients -- Vector and Tensor Operators: Wigner-Eckart Theorem -- Spin-Orbit Interactions -- Hydrogen Atom with Spin in External Fields -- Time-Dependent Problems -- Approximation Techniques in Time-Dependent Problems -- Fermi's Golden Rule