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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 | > + (1-P op )| > = |P > + |(1-P) > where | P > has eigenvalue 1 and |(1-P) > has eigenvalue . Note that the sates |P > and |(1-P) > 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 eigenvalue of A op with the same eigenvalue a ....
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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