In 12/01/12 class meeting: \"If there is no observer, Wigner device is equivalen
ID: 1915692 • Letter: I
Question
In 12/01/12 class meeting: "If there is no observer, Wigner device is equivalent to doing nothing". Now let's prove this statement by algebra. Assume the initial state of the electron spin is |Psi > and the inhomogeneous magnetic field is aligned along the +z and -z direction. Please derive the spin state after the 1st, the 2nd, and the 3rd magnet pair in the Wigner device. (Hint: express |Psi > in terms of the eigenbasis of the Hamiltonian operator.) In predicting the SGx outcomes and in solving PS#5[4], we express |+Sz > and |-Sz> as a linear combination of |+SX> and |-SX>. For examples, |+SZ> = C1| + Sx> + C2|-Sx>. Please derive c1 and c2. Please show algebraic details. (Hint: Express |+SX> and |-SX> in terms of |+Sz> and |-Sz> and then solve for |+Sz>. The following equations may be useful: S |s, m> = [s(s+1)-m(m+1)]1/2 |s,m+1>; S |s, m> = [s(s+1)-m(m-1)]1/2 |s,m-1> where S+ = Sx + iSy, and |s, m> is the common eigenkets of S2 and Sz)Explanation / Answer
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