1. Quantum mechanics II Winter 2012
Physics 452
Quantum mechanics II
Winter 2012
Karine Chesnel

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

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

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

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

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

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

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

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

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

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

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