Physics 424: Quantum Mechanics, Fall 2015 Reading/Homework Assignment 6 Due in Class Monday , 10/26/15 1 Reading • Townsend Sec. 4.4 – Magnetic Resonance • (Townsend Secs. 4.5-4.6 will not be covered in class at this time and are optional reading) • Townsend Sec. 4.7 – Summary • Townsend Sec. 5.1 – Basis States for Two Spin 1/2’s • Townsend Sec. 5.2 – The Hyperfine Splitting • Townsend Sec. 5.3 – The Addition of AM for Two Spin 1/2’s You don’t need the following sections for these HW problems, but we will start discussing these topics in class: • Townsend Sec. 5.4 – The EPR Paradox • Townsend Sec. 5.5 – Bell Inequalities Problems to work out and turn in (75 pts total) 1. (15 pts total) Note: This entire problem is classical (no quantum me- chanics). In class we showed that the classical equation of motion for the spin vector S in an applied field B is d S dt = γ S × B where γ is the gyromagnetic ratio. 1 2015-10-20 P424 HW6.tex c 2015 Donald Candela 1
(a) (5 pts) AssumeB=B0kwherekis the unit vector in the +zdirection. Show that the equations of motion for the three com-ponents ofSaredSxdt=γB0Sy,dSydt=-γB0Sx,dSzdt= 0.(b) (10 pts) Solve these equations of motion to show thati. The magnitude ofSremains constant.ii. The angle betweenSand thez-axis remains constant.iii.Srotates around thez-axis (clockwise looking down the axisifγ >0) at angular frequencyω0=γB0(the Larmor fre-quency).2. (10 pts) This is a simple problem, but it will require you to look upsome numbers and keep your units straight (both useful skills). Thegyromagnetic ratio for the proton isγp= +2.68×108s-1T-1, while
You've reached the end of your free preview.
Want to read all 5 pages?