Physics 115 - Seminar 13December 9, 2002Photons and AtomsComments Townsend chapter 14: This chapter covers too much, but still manages a decent job.It is a good idea to supplement this chapter with other sources, such as Shankar and Loudon. I’llpull material from Shankar’s chapter 18 and Loudon chapters 2 and 4.Presentations1. Two level systems and the Optical Bloch Equations. Present Loudon se ctions 2.1, 2.2, and2.7 (Andrew)2. Problem 7 (Roban)3. Problem 6 (Matt)4. Problem 5 (Mike)5. Problem 4 (Melaku)6. Problem 3 (Mark)7. Problem 2 (Robin)8. Problem 1(Ursula)Problems1. Townsend 14.4 - Solutions to the relativistic version of the Schr¨odinger equation, known asthe Klein-Gordon equation.2. Townsend 14.6 - Perturbed harmonic oscillator - treat the field interaction semi-classicallyH1= −e~r ·~E (exp(iωt) + exp(−iωt))where the harmonic oscillator moves along the x-axis (~r =ˆix) and so p oints the field(~E =ˆiE0).3. Townsend 14.8 - NMR as a perturbation.4. Townsend 14.10 -Magnetic Dipole transitions are isotropic if the measurement isn’t spin-sensitive. Hint: How do the probabilities P+12and P−12depend on Bx, By, and Bz?5. Townsend 14.12 - Photoelectric effect theory.16. Assume that an electron is initially in the ground state |0i of a molecule described by acomplete set of states |ni which are eigenstates of the time-independent Hamiltonian, H0|ni =En|ni. Treat the interaction with radiation “semi-classically” (see Problem 2) and show thatthe coefficients cfarecf=~µf0·~E¯heiωf 0 1 − e−iωtωf0− ω+1 − eiωtωf0+ ω!where ~µf0= −ehf|~r|1i and ¯hωf0= Ef− E0. Use the coe fficie nts to derive and expression forthe wavefunction (to first order, of course) and the dipole moment ~µ = −ehψ|~r|ψi.7. Shankar 18.2.5 - An interesting way to look at the effect of linear potentials on harmonicoscillator