3. An electron is placed at rest in a uniform magnetic field B = Bo2. Initially the electron is in the state |(t = 0)) =

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3 An Electron Is Placed At Rest In A Uniform Magnetic Field B Bo2 Initially The Electron Is In The State T 0 1 (28.34 KiB) Viewed 40 times

3. An electron is placed at rest in a uniform magnetic field B = Bo2. Initially the electron is in the state |(t = 0)) = |+), with n = (-k). (a) What is initial state in the S₂-basis? In other words, if we have (0))= (3), find a and b. (b) Find (t)) (c) What is the probability that the particle will be measured to have spin down in the x-direction after a time t? Sketch the probability as a function of time. It is always useful to check answers - this is a probability, so convince yourself (and us) that your answer always falls in the allowed range for probabilities! (d) Is there ever a 100% chance that the system will get back to its original state? If so, when? If not, why not?