Path Integral Qm
Quantum Field Theory · Part 3
212 KB5 sections4 key equationsLaTeX typeset
Table of Contents
- 1.2.1 The Path Integral Idea
- 2.2.2 Transition Amplitude
- 3.2.3 Example: Free Particle
- 4.What Does "Sum Over All Paths" Mean?
- 5.Key Concepts (This Page)
Key Equations
$$\boxed{K(x_b,t_b;x_a,t_a) = \int \mathcal{D}x(t) \, e^{iS[x(t)]/\hbar}}$$
$$S[x(t)] = \int_{t_a}^{t_b} dt \, L(x,\dot{x},t) = \int_{t_a}^{t_b} dt \left[\frac{1}{2}m\dot{x}^2 - V(x)\right]$$
$$K(x_b,t_b;x_a,t_a) = \lim_{N\to\infty} \int dx_1 \cdots dx_{N-1} \prod_{j=0}^{N-1} \sqrt{\frac{m}{2\pi i\hbar \epsilon}} \exp\left[\frac{i}{\hbar}\epsilon L(x_j, \frac{x_{j+1}-x_j}{\epsilon})\right]$$
$$S[x(t)] = \int_{t_a}^{t_b} dt \, \frac{1}{2}m\dot{x}^2$$
Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.
Course Context
This PDF is part of the Quantum Field Theory course on CoursesHub.World. Free online course in Quantum Field Theory (QFT). 8 parts covering classical field theory, canonical quantization, path integrals, QED, non-Abelian gauge theories, renormalization, the Standard Model,...