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Physics 452

Physics 452. Quantum mechanics II Winter 2012. Karine Chesnel. Phys 452. Homework. 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. Phys 452. Emission and absorption of a radiation. Absorption. Emission.

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Physics 452

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  1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

  2. Phys 452 Homework 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

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

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

  5. Phys 452 Quiz 24a 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

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

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

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

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

  10. 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

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

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

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

  14. 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

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

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

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

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

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