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Unformatted text preview: i times a Hermitian operator. (c) With what restriction on the number Î» is 1 + iÎ»â†’ Ïƒ Â·â†’ n 1iÎ»â†’ Ïƒ Â·â†’ n , (whereâ†’ n * =â†’ n ,â†’ n Â·â†’ n = 1) , a unitary operator? Write this in the form of part (a) and in the form of part (b) . [3] Find the value of Tr ( 1 + ( Ïƒ x + Ïƒ y ) / âˆš 2 2 1 + (Ïƒ x + Ïƒ y ) / âˆš 2 2 ) . What physical meaning can you give to this number? 1 [4] A spin1/2 particle interacts with a magnetic ï¬eldâ†’ B = B Ë† z through the Pauli interaction H = Î¼â†’ Ïƒ Â·â†’ B where Î¼ is the magnetic moment andâ†’ Ïƒ = ( Ïƒ x ,Ïƒ y ,Ïƒ z ) are the Pauli spin matrices. At t = 0 a measurement determines that the spin is pointing along the positive xaxis . What is the probability that it will be pointing along the negative yaxis at a later time t ? 2...
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 Spring '09
 bekir
 Work, #, Hilbert space, Unitary matrix, Pauli spin matrices

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