Time Dependent

Quantum Mechanics · Part 6

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Table of Contents

  1. 1.The Setup
  2. 2.The Interaction Picture
  3. 3.First-Order Perturbation Theory
  4. 4.Transition Probability
  5. 5.Constant Perturbation Turned On at t=0
  6. 6.Sinusoidal Perturbation
  7. 7.Resonance: Absorption and Stimulated Emission
  8. 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 ...

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