28. Consider a harmonically bound electron in 1D with HamiltonianH0=12~ω(q2+p2), initially in its groundstate. A heavy particle passes through the region at high speed. This heavy particle interacts with theelectron through a weak short-range interaction that can be approximated by the potentialV(t)=V0δ(q−x(t)) =V0δ(q−vt),wherevis essentially the velocity of the heavy particle (in dimensionless units of theoscillator), andV0<<~ωis a constant. Sketch the potential seen by the electron for timest<0,t=0,andt>0.Find the probability that the electron is left in thefrst excited state as a result of this collision.Sketch this probability as a function ofv.29. Consider a particle of massmand chargeeconstrained to move on the circumference of a circle of radiusalying in thexy-plane, initially in its ground state. A weak, time-varying, but spatially uniform electricfeld “pulse” is applied of the form~E=E0e−τ2/τ2ˆxwhich has its peak att.Inf
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 463 taught by Professor Paule. during the Fall '10 term at Missouri S&T.