hw.6 - Express your answers in terms of transition dipoles....

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Physics 829 Spring 2001 Dr. Herbst Homework Assignment # 6 Due: 18 May 2001 1) Assuming that the perturbation between electromagnetic radiation and matter in the semi-classical treatment is given by W DE (t) for the polarized radiation studied in class, derive an equation for md 2 /dt 2 < R > where R is the relative position of the electron with respect to the proton. Discuss your result. Hint: remember Ehrenfest’s Theorem. 2) Use the actual semiclassical W(t) derived in class for a plane wave travelling in the y direction along with time-dependent perturbation theory to calculate P fi (t, ϖ ) for absorption and emission in terms of A 0 . Then reduce your answers to the electric dipole approximation by converting A 0 into ε and expanding exp(ikY). Discuss a (gauge-dependent) problem with your solutions as ϖ --> 0. 3) Derive formulae for the one-photon emission and absorption probabilities for an atom in the dipole approximation using one monochromatic mode (in one direction) of the quantized radiation field.
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Unformatted text preview: Express your answers in terms of transition dipoles. Use the long-time limit. 4) Derive the formula for the one-photon spontaneous emission rate in the dipole approximation using a quantized radiation field and the proper three-dimensional density of states formula for the modes of radiation. Use Fermis Golden Rule. 5) An electron moves in the one-dimensional potential V(x) = - (x). At time t=0, the potential suddenly changes to V(x) = - (x). Both and are positive. Calculate the probability of a transition from the old ground state to the new ground state. Consider the special case =/2 and discuss /1 and /1. 6) A harmonic oscillator in its ground state oscillates in one dimension around an equilibrium distance x . Suddenly, the equilibrium distance is changed to x 1 . Determine the probability that the oscillator stays in its ground state....
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This note was uploaded on 06/13/2011 for the course PHYSICS 829 taught by Professor Staff during the Spring '07 term at Ohio State.

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