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assign2 - Problem Set 02 Note This problem set is due Sep...

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Problem Set 02 Note: This problem set is due Sep 20 in the class 1. Consider a Stern-Gerlach experiment with a non-uniform magnetic field B z along the z -axis. The collimator allows the electrons to go along the x -axis uninterrupted if no magnetic field is switched on, and hit the screen kept at a distance L from the collimator. Once the magnetic field is switched on, the electrons get deflected, as we discussed in the class. Now imagine the following modification to the standard Stern-Gerlach experiment: the magnetic field B z is slowly varying wrt time in the following way B z = b ( z ) ( 1 + t 2 ) (1) with 0 being really small and b ( z ) is some given function of z . We also allow the electrons to come out of the furnace at a temperature T so that they have energies pro- portional to T itself. Find an expression for the distance d by which the two spin states would be separated on the screen. 2. Answer the following questions: (a) Given a matrix M such that it is hermitian i.e M ij = M * ji or alternatively M = M , (2) show that the diagonal elements of this matrix are always real numbers.
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