Question 4 An electron is placed in a controllable magnetic field B. The initial spin state of the electron is (v(t = 0)) = \\+). Your goal is to make the spin precess to the state +), by applying uniform magnetic fields. Answer the following questions. (a) Consider the following experiment:. First, you apply a magnetic field B = Bra in the r-direction for a time to, and then turn it off. . Immediately after that, you apply a magnetic field B = B, 2 in the 2-direction for a time tz, and then turn it off. What times t, and t, should you choose to ensure that the final state is |+),? Write your answer in terms of the charge of the electron e, the mass of the electron me, and the magnetic field strengths B, and B. (b) Now consider a different experiment: . Instead of applying the magnetic fields sequentially, you apply them simultaneously with equal strengths. The resultant magnetic field is B = Bri + B,2, where B, = By. You apply this field for a time t, and then turn it off. What time t should you choose to ensure that the final state is ( +),? Write your answer in terms of the charge of the electron e, the mass of the electron me. and the magnetic field strengths B, = B. (c) For B, = B, which of these experiments is quicker to perform? Hint: Use the Bloch sphere picture to reason about this question. You may invoke the general solution for the precession of a spin-, state about the direction of a uniform magnetic field derived in lectures