(9) and (0) 2mo 1. We define to be simultaneous eigenstates of S and S., whose S. eigenvalues are 1/2 and -1/2 respectiv

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9 And 0 2mo 1 We Define To Be Simultaneous Eigenstates Of S And S Whose S Eigenvalues Are 1 2 And 1 2 Respectiv 1 (46.22 KiB) Viewed 28 times

(9) and (0) 2mo 1. We define to be simultaneous eigenstates of S and S., whose S. eigenvalues are 1/2 and -1/2 respectively. In this representation, S = AG.), = 10; 7)S: = 166 -2) Then the Hamiltonian of this electron is .BR 1 A = 5, B = ( 3 ) =< (6 -2). -1 where x = eBh/2m. a) Show that the states energies? b) Using an appropriate mathematical condition, show whether the y component of its spin angular momentum, S, , is conserved. Note that you must demonstrate this by explicitly evaluating your mathematical condition. c) Show that are eigenstates of S. What are their normalization factors and eigenvalues? d) Atr=0, a measurement of S, on the electron yields – /2. What is the probability of getting - h/2 if you measure S, again at a later time t (note: not immediately)? Simplify your answer as much as you can. Remember that it has to be a real number. You are given the formula e = cos 0+isino. (9) and (9) are stationary states. What are their