Time Dependent
Quantum Mechanics · Part 6
220 KB8 sections4 key equationsLaTeX typeset
Table of Contents
- 1.The Setup
- 2.The Interaction Picture
- 3.First-Order Perturbation Theory
- 4.Transition Probability
- 5.Constant Perturbation Turned On at t=0
- 6.Sinusoidal Perturbation
- 7.Resonance: Absorption and Stimulated Emission
- 8.The Energy-Time Uncertainty Principle
Key Equations
$$\hat{H}(t) = \hat{H}_0 + \hat{H}'(t), \quad \hat{H}'(t) = 0 \text{ for } t < 0$$
$$c_m(0) = \delta_{mi} \quad \Rightarrow \quad c_m^{(0)}(t) = \delta_{mi}$$
$$c_f^{(1)}(t) = \frac{V_{fi}}{i\hbar}\int_0^t e^{i\omega_{fi}t'}\, dt' = \frac{V_{fi}}{i\hbar}\frac{e^{i\omega_{fi}t} - 1}{i\omega_{fi}}$$
$$c_f^{(1)}(t) = \frac{V_{fi}}{2i\hbar}\left[\frac{e^{i(\omega_{fi}+\omega)t}-1}{\omega_{fi}+\omega} + \frac{e^{i(\omega_{fi}-\omega)t}-1}{\omega_{fi}-\omega}\right]$$
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 ...