Intro to Quantum Mechanics II

(3 Credit Hours) · Undergraduate

The purpose of this course is to derive relativistic equations which describe quantum systems and understand their relationship with symmetries and group theory. [Advanced Quantum Mechanics] Addition of angular momentum. Spin angular momentum. Introduction to the standard model of particle physics. [Symmetries and Group Theory] Abstract groups and their representations. Lie groups and infinitesimal generators. Lie algebras. [Spacetime Symmetries] The Lorentz group. The Poincare group. Casimir operators. [Relativistic Wave Equations] Maxwell's equations and gauge theory. The lack of Lorentz invariance of the Schrodinger equation. The Klein-Gordon equation. [The Dirac Equation] Properties of the Dirac equation. The non-relativistic limit. Spinors. Negative-energy solutions: hole theory and anti-particles. [Relativistic Scattering] The free solution of the Dirac equation. The time-independent Dirac equation. The Dirac equation in the presence of a potential. [Introduction to Quantum Field Theory] The Klein-Gordon field.