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Unformatted text preview: Physics 225/315 January 21, 2008 Operators Matrix Representation An operator transforms a state. A  =  . Expand the states in the z basis.  =  + +  +    =  + +  +   Then A  =  bcomes A (  + +  +   ) =  + +  +   Take the inner product with +  and also with +  A  + +  + +  A   = +   A  + +  + A   = Write this as a matrix equation. +  A  + +  A  A  + A  ! +   ! = +   ! Average value The operator A is associated with the measurement of an observable. Expand operator A , as a spectral decomposition in terms of projection operators on basis states. A =  + a + +  +  a where a + and a are the measured values of the observable in each of the two basis states. For components of spin a + = h 2 and a = h 2 Evaluate  A  =  + +  a + +   a = P + a + + P a where P + and P are the probabilities for finding each of the basis states....
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 Spring '10
 ROTHBERG
 Physics

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