Fine Structure
Quantum Mechanics · Part 6
216 KB10 sections4 key equationsLaTeX typeset
Table of Contents
- 1.The Fine Structure Constant
- 2.Three Relativistic Corrections
- 3.1. Relativistic Kinetic Energy
- 4.2. Spin-Orbit Coupling
- 5.Total Angular Momentum
- 6.3. Darwin Term
- 7.Combined Fine Structure Formula
- 8.Energy Levels with Fine Structure
- 9.Example: n=2 Level Splitting
- 10.Lamb Shift
Key Equations
$$\alpha = \frac{e^2}{4\pi\epsilon_0\hbar c} \approx \frac{1}{137.036}$$
$$E_r^{(1)} = -\frac{(E_n)^2}{2mc^2}\left[\frac{4n}{\ell + 1/2} - 3\right]$$
$$\vec{L}\cdot\vec{S} = \frac{1}{2}(\hat{J}^2 - \hat{L}^2 - \hat{S}^2) = \frac{\hbar^2}{2}[j(j+1) - \ell(\ell+1) - s(s+1)]$$
$$\hat{H}'_D = \frac{\pi\hbar^2 ke^2}{2m^2c^2}\delta^3(\vec{r})$$
Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.
Course Context
This PDF is part of the Quantum Mechanics course on CoursesHub.World. Master quantum mechanics from mathematical foundations to advanced topics. Covers Hilbert spaces, wave functions, angular momentum, perturbation theory, scattering, and path integrals with 450+ pages ...