2. An electron in a magnetic eld [10 pts]. Imagine that we have an electron in a spatially-varying magnetic eld in which B = ax2 and a = 10 G/mm2. Assume that the eld is in the up (+y) direction to which the spin is either aligned ( up ) or anti-aligned ( down ). (a) What is the energy of the electron in each spin state as a function of position x [2 pts]? (b) Which of the two spin states is trapped in the magnetic eld, meaning that a stable equilibrium exists with the electron at x = 0 [2 pts]? What will happen to electrons in the other spin state? [2 pts] (c) What is the transition frequency between the two spin states as a function of position x [2 pts]? Assuming that the electron is initially in the trapped spin state, what frequency could selectively untrap and eject the electron at a position of exactly x = 2 mm [2 pts]