Relativistic Quantum Mechanics: Spin & Dirac Equation

Delve into the fascinating world of Relativistic Quantum Mechanics with this comprehensive course! While Quantum Mechanics (QM) and Quantum Field Theory (QFT) are foundational, this course offers a focused exploration of concepts not typically covered in introductory QM/QFT courses.

This course builds upon a solid understanding of operators and commutators, essential for grasping how measurements of physical quantities are linked. We begin by examining commutation relations related to angular momentum, leading to a clear derivation of the concept of spin.

The course then leverages these concepts to construct the Dirac equation, a cornerstone of relativistic quantum mechanics. You'll discover how spin is naturally integrated into a relativistic framework.

Next, we tackle the Dirac equation by solving it for a free particle. We'll derive important conserved quantities such as the Hamiltonian and current from this equation.

Finally, using further commutation relations, we'll unlock the spectrum of the hydrogen atom in the relativistic regime and compare it to the familiar non-relativistic solution.

Prerequisites: A good understanding of operators and commutators is recommended.

Key topics covered:

• Angular Momentum & Spin: Explore the fundamental relationship between angular momentum and intrinsic angular momentum (spin).
• Dirac Equation: Learn to construct and solve the relativistic wave equation.
• Relativistic Quantum Mechanics: Understand how quantum mechanics adapts to relativistic principles.
• Spin in Relativistic Theory: See how spin is naturally incorporated into the Dirac equation.
• Conserved Quantities: Derive the Hamiltonian and current from the Dirac equation.
• Hydrogen Atom Spectrum (Relativistic): Calculate and compare the relativistic hydrogen atom spectrum with the non-relativistic result.