bra-ket-handout - Chem. 540 Nancy Makri Dirac bra-ket...

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Unformatted text preview: Chem. 540 Nancy Makri Dirac bra-ket notation The symbol n (or n ) is called a ket and denotes the state described by the wavefunction n . The complex conjugate of the wavefunction, n , is denoted by the bra n (or n ). The ket denotes a state in the most abstract form, without reference to a particular representation. When we put a bra together with a ket, with an operator in the middle, we imply integration over all space: ( ) ( ) or n m n m d A A n A m r r r Leaving out the operator implies the identity operator, i.e., ( ) ( ) m n m n n m d = r r r m n is the amplitude for a particle in state n to be also in state m . This is also known as the overlap of these two states. In this notation, the condition for an operator to be hermitian is m n n m A A = . Remarks n m is a scalar (i.e., a number)....
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This note was uploaded on 02/08/2012 for the course CHEM 540 taught by Professor Mccall during the Fall '08 term at University of Illinois, Urbana Champaign.

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bra-ket-handout - Chem. 540 Nancy Makri Dirac bra-ket...

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