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Unformatted text preview: Physics 225/315 January 25, 2008 Hermitian Operators Hermitian Adjoint An operator transforms a state. A  =  . The hermitian adjoint A transforms the corresponding dual state.  =  A . If A = A the operator or matrix is hermitian. The hermitian adjoint of a matrix is the complex conjugate transpose. Expectation value of a hermitian operator is real The relationship between a state and its dual is  =  *  A  * =  * =  =  A  Then  A  =  A  * If A = A then  A  =  A  * and if  =  then  A  is real . This is the expectation value of A in the state  . Eigenvalues of a hermitian operator are real A  =  Take inner product with  then  A  =  The expectation value is real and  is real so is real. The spin operators S x , S y , S z are hermitian and all have eigenvalues h 2 ....
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 Spring '10
 ROTHBERG
 Physics

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