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Unformatted text preview: i times a Hermitian operator. (c) With what restriction on the number Î» is 1 + iÎ»-â Ï Â·-â n 1-iÎ»-â Ï Â·-â n , (where-â 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) .  Find the value of Tr ( 1 + ( Ï x + Ï y ) / â 2 2 1 + (-Ï x + Ï y ) / â 2 2 ) . What physical meaning can you give to this number? 1  A spin-1/2 particle interacts with a magnetic ï¬eld-â B = B Ë z through the Pauli interaction H = Î¼-â Ï Â·-â B where Î¼ is the magnetic moment and-â Ï = ( Ï x ,Ï y ,Ï z ) are the Pauli spin matrices. At t = 0 a measurement determines that the spin is pointing along the positive x-axis . What is the probability that it will be pointing along the negative y-axis at a later time t ? 2...
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- Spring '09
- Work, #, Hilbert space, Unitary matrix, Pauli spin matrices