Homework Problems

1. A hydrogen atom is placed in an electric field which is uniform in space and turns on at then decays exponentially. That is, for and for . What is the probability that, as , the hydrogen atom has made a transition to the state?

2. A one dimensional harmonic oscillator is in its ground state. It is subjected to the additional potential for a a time interval . Calculate the probability to make a transition to the first excited state (in first order). Now calculate the probability to make a transition to the second excited state. You will need to calculate to second order.

Jim Branson 2013-04-22