Gerrit-Jan Linker
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Completeness relation or closure relation The completeness relation or also called closure relation is often used in the algebra in quantum mechanics: Σi |si><si| = 1 = 1 Suppose we have a complete set of orthonormal functions (states) |si> An arbitrary function Ψ can be written as a linear combination: |Ψ>=Σici|si> Multiplying both sides by <sj| gives: <sj|Ψ> = <sj|Σici|si> <=> <sj|Ψ> = Σici<sj|si> = Σiciδji = cj <=> <sj|Ψ> = cj Thus, |Ψ> = Σici|si> = Σi<si|Ψ>|si> = Σi|si><si|Ψ> <=> |Ψ> = (Σi|si><si|) |Ψ> thus, Σi|si><si| = 1 = 1
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