Physics 452

1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

2. Phys 452 Tuesday Mar 13: assignment # 15 Pb 9.7, 9.18, 9.19 Homework Friday Mar 9: assignment # 14 Pb 9.1, 9.2, 9.5, 9.6

3. Phys 452 Two- level systemsTime- dependent perturbation In case of off-diagonal perturbation

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

5. Phys 452 Two- level systemsTime- dependent perturbation Initial conditions: Goal: solve for ca and cb First order:

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

7. Phys 452 Two- level systemsTime- dependent perturbation Application: sinusoidal perturbation Initial conditions First order Probability of transition:

8. Phys 452 Two- level systemsTime- dependent perturbation Sinusoidal perturbation Probability of transition: P(t) for a given frequency w t

9. Phys 452 Two- level systemsTime- dependent perturbation Sinusoidal perturbation Probability of transition: P(w) for a given time t w

10. Phys 452 Two- level systemsTime- dependent perturbation P(w) w Pb 9.7 Solving exactly for Probability of transition: Rabi flopping frequency

11. Phys 452 Time- dependent perturbation Pb 9.1 Electric field perturbation n=2 n=1 Simulation of atomic dipole transition www.falstad.com/qmatomrad/

12. Phys 452 Time- dependent perturbation Apply this theory for time-independent perturbation Pb 9.2 Second order differential equation Transition between two states still possible

13. Phys 452 Time- dependent perturbation Apply this theory for time-independent perturbation Pb 9.6 Use the perturbation theory And integrate at second order Compare with the exact answer of problem 9.2

14. Phys 452 Time- dependent perturbation Two levels system with different initial conditions Pb 9.5 Initial conditions