I2

An electron is placed in a controllable magnetic eld E. The initial spin state of the electron is |11)(t = 0)) = |+). You would like to cause the spin to precess to the state |+)m by applying uniform magnetic elds. Answer the following questions. 1. Consider the following experiment. First, you apply a magnetic eld B" = BE}? in the $- direction for a time t3, and then turn it o". After that, you apply a magnetic eld B' = 3,2 in the z-direction for a time 752, and then turn it off. What times 75,, and it, should you choose to ensure that the nal state is |+),,? Give your answer in terms of the charge of the electron e, the mass of the electron me, and the magnetic eld strengths B,D and B2. Hint: Remember that quantum states are equivalent up to an overall phase. 2. Now consider a different experiment. Instead of applying the magnetic elds sequentially, you apply them simultaneously. The resultant magnetic eld is E = Bzi -| Bait, where B1: = Bz. You apply these elds for some time t, and then turn both elds off. What time t should you choose to ensure that the nal state is |+) 1.? Give your answer in terms of the charge of the electron e, the mass of the electron me, and the magnetic eld strengths Ba, and Bz. 3. If the magnetic eld strengths are 8,, = 3,, = 10 mT, which of these experiments is quicker to perform? Hint: Use the Bloch sphere as a tool to avoid unnecessary calculations