1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

2. Phys 452 Homework Friday Mar 9: assignment # 14 9.1, 9.2, 9.5, 9.6

3. Phys 452 Quantum jumps… Lifetime of excited states… Oscillation between states… Time-dependent Schrödinger equation How to describe dynamical phenomena ? Simulation of atomic dipole transition www.falstad.com/qmatomrad/

4. Phys 452 Quiz 21 In case of time-independent Schrödinger equation, the solution for the wave function y does not depend on time • True • False

5. Phys 452 “Static” potential Eigenstates: General solution: Probability to measure the energy En: Potential V constant in time

6. Phys 452 Dynamical systems General solution: Probability to measure the energy En and to find the particle in state : V depends on time

7. Phys 452 Time-dependent part Approximation Dynamical systemssolved byperturbation theory

8. Phys 452 Solution for unperturbed state: Two- level systems

9. Phys 452 Two- level systemsTime- dependent perturbation Perturbed state: Perturbation theory: Apply:

10. Phys 452 Two- level systemsTime- dependent perturbation Perturbed state:

11. Phys 452 Two- level systemsTime- dependent perturbation In case of off-diagonal perturbation with Perturbation matrix

12. Phys 452 Two- level systemsTime- dependent perturbation Approximation: At first order: Goal: solve for ca and cb

13. Phys 452 Two- level systemsTime- dependent perturbation First order: Zeroth order = Initial conditions:

14. Phys 452 Two- level systemsTime- dependent perturbation Second order:

15. Phys 452 Two- level systemsTime- dependent perturbation Zero order: First order: Second order:

16. Phys 452 Express , , , and Calculate Selection rules for Electric dipolar transition Non-zero terms Two- level systems Pb 9.1 Hydrogen atom and electrical field

17. Phys 452 Two- level systems Pb 9.2 Application to time-independent perturbation with