PHYS212 : Homework


Homework Assignment 10 (due 4/27)

Time Dependent Perturbation Theory, Selection Rules, and Transition Rates

  1. (a) Calculate the lifetimes of the first three excited states ($n = 2,3,4$) of an electron in an infinite square well of width $L = 1.0$ nm. Assume only E1 transitions give significant transition rates.

    Note: The $n = 4$ state can de-excite via two different E1 transitions, so you need to use Eq. 7.149.

    (b) What are the branching ratios

    \begin{displaymath}
BR_{i \rightarrow f} = \frac{r_{i \rightarrow f}}
{\displaystyle\sum_{f'} r_{i \rightarrow f'}}
\end{displaymath}

    of the two E1 decay modes of the $n = 4$ state?

  2. Determine the selection rules for transitions triggered by an oscillating delta function perturbation located at the center of an infinite square well,

    \begin{displaymath}
\hat{U}(x,t) = U_o \delta(x-L/2)   \cos(\omega t)
\end{displaymath}

Lab 4: The Labyrinth


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