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

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

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

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

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

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

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:

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

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

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

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

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

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

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

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

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

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

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