Physics 115 - Seminar 9November 8, 2002Applications of Spin Quantum MechanicsComments Townsend chapters 4, 5 and 8: Chapters 4 and 5 present applications of spin quantummechanics to problems of magnetic interaction (spin precession, NMR), electric field interaction, andhyperfine splitting along with some interesting discussion of the EPR Paradox and Bell Inequalities.Presentations1. Problem 1 (Andrew)2. Problem 2 (Roban)3. Problem 3 (Matt)4. Problem 4 (Mike)5. Problem 6 (Melaku)6. Problem 7 (Mark)7. Problem 8 (Robin)8. Problem 9 (Ursula)Problems1. Townsend 4.1 and 4.8 - Magnetic dipole interaction2. Townsend 4.10 - Electric dipole interaction3. Townsend 4.13 - Three level system4. Townsend 5.1 - hyperfine splitting, this is a nice problem that can be solved exactly. In thelimiting cases, approximate solutions can be derived that are a good test for perturbationtechniques (we’ll see them next week).5. Townsend 5.2 and 5.3 - Simple addition of angular momenta.6. Townsend 5.5 - Positronium7. Townsend 5.7 - Polarization States8. Townsend 8.1 - Path integral propagator for a gaussian wave packet.9. Like Townsend 8.1 but with momentum. Consider a gaussian wave packet with a centralmomentum p0and a variance ∆p,1hp|ψi =1q∆p√πexp"−(p − p0)22∆2p#It is fairly straight forward to put |ψi in the position basis and gethp|ψi =s∆p√πexp"−x2∆2p2¯h2#expip0x¯hUse the propagator for the free-particle (8.9) to determine how the packet evolves with time.Note: the center of the wave packet should follow a classical