10.1. (a) Show that (10.2.21) follows from (10.2.19) in the limiting case of a two-state atom. (b) Now consider, instead of the two-state model, a nonlinear electron oscillator model in which

(3.2.18b) is replaced by d²x dt² +w√x + ax" = - Eo cos wt m in the case of an applied field of frequency w. Find, for n = 2, the solution for the induced dipole moment ex including terms up to second order in the field amplitude Eo. (c) For this nonlinear oscillator model with n = 3, find the solution for the induced dipole moment including terms up to third order in Eo./n(50 points) Consider the nonlinear electron oscillator model x+w²x + ax" = Eo cos wit m where Eo is the field amplitude, w₁ is the driving laser frequency, wo is the resonance, and n is an integer. This problem is part (b) and (c) of question 10.1 from the textbook. (a) Find, for n = 2, the solution for the induced dipole moment, ex, inluding terms up to second order in the field amplitude Eo. (b) For this nonlinear oscillator model with n = 3, find the solution for the induced dipole moment including terms up to third order in Eo. (c) Sketch (just sketch, don't need to plot) the potentials for n = 2 and n = 3.