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Unformatted text preview: = = and where the are eigenfunctions of the parity operator with eigenvalues 1 as follows: ) ( ) ( x x P op = . Parity Conservation: Since the P operator has no explicit time dependence we have ] , [ op op H P dt P d i = > < h Thus, if the Hamiltonian H is symmetric under x -x then [P op ,H op ] = 0 parity is a constant of the motion ( i.e. it is conserved ). Projection Operators: The operators ) 1 ( 2 1 op op P P = project out the states with definite parity. In general, projection operators have the properties: = op op P P 2 ) ( and = = + + op op op op P P P P ....
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.
- Spring '07