Lecture16

# d r r ri r rsin cos 0 f 10 generic

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Unformatted text preview: ss at how to do a quantum mechanical calculaEon of the rate would be to replace ! ! 3! *!! r ! # " (r )r" (r )d r But because this is a transiEon, it should involve BOTH iniEal and ﬁnal states. The correct way to proceed is to write: ! ! 3! *!! r ! # " f (r )r" i (r )d r Final state wavefuncEon iniEal state wavefuncEon 15 SelecEon rules ! !! ! ! r ! # " * (r )r" i (r )d 3r f Due to the angular part of the wavefuncEon (spherical harmonics), some integrals will be 0 Example: transiEons between 2 ! = 0 states: % # 2# 0 0 0 r 2 dr \$ sin(! ) d! \$ d " R* (r ) Ri (r )(rsin(! )cos(" )) =0 f \$ 1.0 Generic properEes of spherical harmonics lead to transiEons only being allowed for 0.5 1 2 3 4 5 6 Area = 0 !! = 1 ￿0.5 ￿1.0 Angular momentum of electron must change by a unit of ħ 16 TransiEons and photon emission N2 = populaEon of excited state N1 = populaEon of ground state Rate at which the excited state spontaneously decays to the ground state is proporEonal to the number of excited atoms. dN 2 = ! RN 2 (t ) dt N 2 (t ) = N 0 e! Rt 17 Photons in a cavity Photons ar...
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