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

5. Homework Phys 452 Friday Mar 16: assignment # 16
9.8, 9.9, 9.10, 9.12, 9.14
Tuesday Mar 20: assignment # 17
9.17, 9.20, 9.21

6. Emission and absorption of a radiation
Phys 452
Emission and absorption of a radiation
Interaction between the atom and electromagnetic wave
Absorption
Emission

7. Emission and absorption of a radiation
Phys 452
Emission and absorption of a radiation
Expression for the perturbation
Assuming the wavelength
of the light is large
In comparison to the atom z x y
with

8. Quiz 24a Phys 452 Because emission can be both
stimulated and spontaneous,
and has to counterbalance absorption
in a system at equilibrium,
the stimulated rate of emission has to be smaller than
the stimulated rate of absorption
A. True
B. False

9. Emission and absorption of a radiation
Phys 452
Emission and absorption of a radiation
Probability of absorption
Probability of emission

10. Emission and absorption of a radiation
Phys 452
Emission and absorption of a radiation
Spontaneous emission
No incident light
to stimulate the emission
Natural de-excitation: explained by the presence
of zero-point radiation (quantum electrodynamics)
What are the different rates
of absorption / emission?
All processes together:

11. Stimulated emission and absorption: Transition rate
Phys 452
Stimulated emission and absorption: Transition rate
Take into account the non-monochromaticity of the light

12. Stimulated emission and absorption: Transition rate
Phys 452
Stimulated emission and absorption: Transition rate
Account for the isotropy of emission/absorption process in 3D y z x p
with

13. Emission and absorption: Einstein coefficients
Phys 452
Emission and absorption: Einstein coefficients
: stimulated absorption
: stimulated emission
: spontaneous emission rate
Thermal
equilibrium
Boltzman distribution of particles
Analogy with Planck’s blackbody formula

14. Emission and absorption: Einstein coefficients
Phys 452
Emission and absorption: Einstein coefficients
Pb 9.8: competition between
stimulated and spontaneous
emission...
Comparing the two processes
Find the critical T at given w
or the critical w at given T
for which
Planck’s blackbody radiation

15. Emission and absorption: Einstein coefficients
Phys 452
Emission and absorption: Einstein coefficients
Pb 9.9: deriving spontaneous
emission as a stimulated process
The density of zero-point radiation:
occupation number = 1
in blackbody radiation formula (5.111)
Retrieve expression
for A

16. Spontaneous emission: Lifetime of excited state
Phys 452
Spontaneous emission: Lifetime of excited state
Overpopulated excited state,
not at equilibrium
Lifetime of excited state
When several decay modes

17. Spontaneous emission: Lifetime of excited state
Phys 452
Spontaneous emission: Lifetime of excited state
Pb 9.10: Notion of “half-life”
“Half-life” = Time it takes for half the atoms
to transit back to ground state
Compare t1/2 and t

18. Quiz 24b Phys 452 Selection rules determines if a transition
between two states is allowed or not
A. True
B. False

19. Emission and absorption Selection rules
Phys 452
Emission and absorption Selection rules
Is the transition possible or not?
Yes, only if
The transition is possible only if

20. Emission and absorption Selection rules
Phys 452
Emission and absorption Selection rules
Is the transition possible or not?
Each transition is only possible if
Each condition reduces to

21. Emission and absorption Selection rules
Phys 452
Emission and absorption Selection rules
The transition is only possible if
Case of atomic levels: or