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Unformatted text preview: dual space ). Projection Operators: If  α > is a ( normalized ) “ket” vector. Then the operator (P i ) op =  ψ i >< ψ i  projects out the portion of any “ket” vector that “lies along”  ψ i > . Namely, ( P i ) op  α > =  ψ i >< ψ i  α > = a i  ψ i > , where a i = < ψ i  α > . The operator ( P i ) op is the projection operator onto the onedimensionalspace spanned by  ψ i > . The sum over all the projection operators ( P i ) op gives 1   ) ( 1 1 = >< = ∑ ∑ = = n i i i n i i P where 1 is the identity operator. This is the condition necessary for  ψ i > to form a complete set of states. It is true since > = > >< ∑ =    1 n i i i . Completeness condition!...
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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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