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Unformatted text preview: PH 216, Problem set 7, Due 5/26 1. Consider the elastic scattering of photons off electrons in atoms, assuming that the incident photon energies are large compared to the atomic binding energies. However, you should assume that the photon wavelength is still substantially larger than a typical atomic radius. (a) Using the quantum theory of radiation, argue that the A field operator must occur at least twice in the matrix element in order that there be a non-zero contribution in perturbation theory. (b) Recall that there is a quadratic A A term in the interaction Hamiltonian. Compute the differential cross-section to first order perturbation theory in the dipole approximation. Show that: d 2 ^ ^ = r0 | |2 , d where r0 e2 /(mc2 ) is the classical radius of the electron. (c) Compute the total cross-section, assuming that the initial photon beam is unpolarized and the polarization of the final state photon is not measured. 2. Suppose a hydrogen atom is somehow prepared in the 2P state, and it is known that the value of Lz is definitely +1, that is, the atom is in the state m = 1. (a) Calculate the differential decay rate into any solid angle d. (b) Integrate over all angles and check that the total rate is the same as the one computed class. 6 ...
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This document was uploaded on 10/31/2011.
- Spring '09