[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.