Relativistic

Quantum Mechanics · Part 9

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Table of Contents

  1. 1.Klein-Gordon Equation
  2. 2.Dirac Equation Derivation
  3. 3.Dirac Equation in Covariant Form
  4. 4.Properties and Interpretation
  5. 5.Free Particle Solutions
  6. 6.Non-Relativistic Limit
  7. 7.Antimatter Prediction
  8. 8.Hydrogen Atom with Dirac Equation
  9. 9.Limitations and QFT

Key Equations

$$\left(\frac{1}{c^2}\frac{\partial^2}{\partial t^2} - \nabla^2 + \frac{m^2c^2}{\hbar^2}\right)\phi = 0$$
$$\gamma^0 = \beta, \quad \gamma^i = \beta\alpha^i$$
$$j^\mu = \bar{\psi}\gamma^\mu\psi = \psi^\dagger\gamma^0\gamma^\mu\psi$$
$$u^{(1)} = \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix}, \quad u^{(2)} = \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix}, \quad v^{(1)} = \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix}, \quad v^{(2)} = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix}$$

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 ...

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