Relativistic Quantum Mechanics: Spin & Dirac Equation

Relativistic Quantum Mechanics: Spin & Dirac Equation

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This is a course on Relativistic Quantum Mechanics. Why did I create this new course even if there is already a course on Quantum Mechanics and Quantum Field Theory? The answer is simple: the main reason is that I am passionate about these topics, but another reason is the fact that my previous course on QM and QFT already contained roughly 40 hours of content, so it would have been too "chaotic" if I added another 11-12 hours of content.

Besides, this course is developed on its own (even if we do not start from scratch). In fact, the topics covered here are not covered in the other course. Here we start from some commutation relations regarding angular momentum, from which we derive the concept of spin. It is therefore recommended to have a prerequisite knowledge of operators and commutators, and how the latter are related to the possibility of measuring two physical quantities simultaneously.

After a first part on angular momentum (in particular, intrinsic angular momentum), we use the concepts therein developed to construct the Dirac equation. We will see that the concept of spin is naturally incorporated into the relativistic theory.

Once we have the Dirac equation, we will start solving it in the case of a free particle, and we also derive conserved quantities from it (the Hamiltonian, current, etc.).

From other commutation relations that we derive, we finally find the spectrum of the hydrogen atom in the relativistic case, and compare it with the non-relativistic solution.