An electron is in the lowest state of a GaAs quantum well of width 15nm, which can be treated as an infinitely deep one-dimensional system. Suddenly the middle 5 nm becomes 100 meV deeper. Use the golden rule to derive an expression for the rate at which the electron scatters into other states, and evaluate the rate for the lowest allowed transition. How would the result differ if the middle rose instead of fell, and does perturbation theory look appropriate?
Repeat the calculation of scattering rates, supposing that the initially flat-bottomed well was suddenly tilted by an electric field F = 1 MV m-1. How is this calculation related to that in Section 7.2.2 for the energy levels of a quantum well in an electric field?