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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 one-dimensional-space 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