[b] Plot the spectral density, D[], for a fixed value of & and several different values of T. (Put these all on the

same plot, carefully labeling everything.) These plots should make clear that a finite lifetime, 1, implies a finite

line width--i.e. a spectrum that peaks at & but is spread out in a Gaussian-like distribution around this energy

as shown below./nKDmax

A

SE

Dmax

2

Verify that the width of the distribution, is equal to 1/7 at the half-height of the peak. This is typically inter-

preted as the range of energies that you might expect to measure in an experiment. It implies that

τ δε = 1.

(4)

This is called the Lifetime Broadening Relation, and it should call to mind the time-energy uncertainty relation.

Explain what the LB Relation says about the certainty with which you can know the excited state energy as a

function of the lifetime of the excited state. Look at the two extremes, zero lifetime and infinite lifetime, to help

elucidate the physics.