homework8 - 28. Consider a harmonically bound electron in...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
28. Consider a harmonically bound electron in 1D with Hamiltonian H 0 = 1 2 ~ ω ( q 2 + p 2 ), initially in its ground state. A heavy particle passes through the region at high speed. This heavy particle interacts with the electron through a weak short-range interaction that can be approximated by the potential V ( t )= V 0 δ ( q x ( t )) = V 0 δ ( q vt ) , where v is essentially the velocity of the heavy particle (in dimensionless units of the oscillator), and V 0 << ~ ω is a constant. Sketch the potential seen by the electron for times t< 0 ,t =0 , and t> 0 . Find the probability that the electron is left in the f rst excited state as a result of this collision. Sketch this probability as a function of v . 29. Consider a particle of mass m and charge e constrained to move on the circumference of a circle of radius a lying in the xy -plane, initially in its ground state. A weak, time-varying, but spatially uniform electric f eld “pulse” is applied of the form ~ E = E 0 e τ 2 / τ 2 ˆ x which has its peak at t . In f
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online