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

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

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

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

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

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

7. Dynamical systems solved by perturbation theory
Phys 452
Dynamical systems solved by perturbation theory
Time-dependent part
Approximation

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

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

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

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

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

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

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

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

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

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