Fine Structure

Quantum Mechanics · Part 6

216 KB10 sections4 key equationsLaTeX typeset
Download PDFRead Online (Free)

Table of Contents

  1. 1.The Fine Structure Constant
  2. 2.Three Relativistic Corrections
  3. 3.1. Relativistic Kinetic Energy
  4. 4.2. Spin-Orbit Coupling
  5. 5.Total Angular Momentum
  6. 6.3. Darwin Term
  7. 7.Combined Fine Structure Formula
  8. 8.Energy Levels with Fine Structure
  9. 9.Example: n=2 Level Splitting
  10. 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 ...

← Fermis Golden
Time Dependent →

Get Instant Access to 461+ PDF Study Guides

Professional LaTeX-typeset PDFs with complete derivations, worked examples, and beautiful equation rendering. Download any PDF, anytime. Cancel anytime.

$5
per month
All courses included
Save 17%
$50
per year
Best value
Subscribe Now
Secure payment via StripeCancel anytimeInstant access