Relativistic
Quantum Mechanics · Part 9
237 KB9 sections4 key equationsLaTeX typeset
Table of Contents
- 1.Klein-Gordon Equation
- 2.Dirac Equation Derivation
- 3.Dirac Equation in Covariant Form
- 4.Properties and Interpretation
- 5.Free Particle Solutions
- 6.Non-Relativistic Limit
- 7.Antimatter Prediction
- 8.Hydrogen Atom with Dirac Equation
- 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 ...