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Unformatted text preview: Quantum Mechanics I, Physics 3143: Assignment 8, Fall 2010 1 . (a) The spin-1/2 operators act on a vector space C 2 of state vectors. Find the normalized eigenvectors and eigenvalues of the Pauli matrices, x = 0 1 1 0 , y = i i and z = 1 1 . Clearly, these eigenvectors are also eigenvectors of the spin-1/2 angular momentum operators S x = planckover2pi1 x / 2, S y = planckover2pi1 y / 2 and S z = planckover2pi1 z / 2 , corresponding to the eigenvalues planckover2pi1 / 2 in each case. Let the eigenvectors be labelled, ( x ) , ( y ) and ( z ) , respectively. (b) The system is prepared in the state with normalized vector = a b , where | a | 2 + | b | 2 = 1. Suppose a measurement of the observable S y is made. Calculate the probabilities, |( ( y ) | )| 2 , to find the eigenvalues corresponding to spin up or down along the y-axis, respectively....
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This note was uploaded on 01/22/2012 for the course PHYS 3143 taught by Professor Kennedy during the Fall '10 term at Georgia Institute of Technology.
- Fall '10