Unformatted text preview: − Φ = Φ − = Φ − and where the Φ ± are eigenfunctions of the parity operator with eigenvalues ±1 as follows: ) ( ) ( x x P op ± ± Φ ± = Φ . 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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 Spring '07
 FIELDS
 mechanics, Fundamental physics concepts, Hilbert space, parity operator

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