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Unformatted text preview: The subspace on which it projects is the subspace with eigenvalue 1 . P op  > =  > and 0 = (P op 2 P op ) > = ( 2 ) > Hence = 1 or = 0 . Any state can be written an  > = P op  > + (1P op ) > = P > + (1P) > where  P > has eigenvalue 1 and (1P) > has eigenvalue . Note that the sates P > and (1P) > are orthogonal. Commuting Operators: Consider an hermitian operator H op with satisfying an eigenvalue equation H op  a > = a a > If [A op ,H op ] = 0 then H op A op  a > = H op  A a > = A op H op  a > = aA op  a > = a A a >. Hence, the state A a > = A op  a > is also an eigenket of H op with the same eigenvalue a ....
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.
 Spring '07
 FIELDS
 mechanics

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