Quantum Mechanics · Chapter 25

Relativistic quantum mechanics

What changes when particles move near the speed of light. Lorentz symmetry, the Klein–Gordon equation and its trouble with probability, Dirac’s first-order equation with its gamma matrices and four-component spinors, antiparticles, the non-relativistic limit that gives spin its magnetic moment of exactly two, and the fine structure of hydrogen.

E^{2} = p^{2} c^{2} + m^{2} c^{4}

(□ + m^{2}) ψ = 0

(i ℏ γ^{μ} \partial_{μ} - m c) ψ = 0

ψ ˉ = ψ^{†} γ^{0}

Lessons

Build the foundation

The negative energies would not go away, and an electron could apparently fall into them for ever, radiating as it went.

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08The non-relativistic limitPut the Dirac equation in an electromagnetic field and ask what it says about a slow electron.Read lesson →

09Fine structureThe three corrections from the Dirac equation shift hydrogen’s levels at order $\alpha^{4}mc^{2}$, a few hundred-thousandths of the binding energy, and they can be computed with first-order perturbation theory in the hydrogen states.Read lesson →

10Chapter practiceBring the chapter together: relativistic energies, Lorentz symmetry, the Klein–Gordon and Dirac equations, gamma matrices, spinors, antiparticles, the non-relativistic limit and hydrogen’s fine structure. No worked example sits above the answers.Read lesson →

Mapping the lesson.

Relativistic quantum mechanics

Build the foundation