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IndepndE

IndepndE - Many Electron Atoms-Independent Electron...

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Many Electron Atoms-Independent Electron Approximation-Helium r r r 1 2 12 ++ - - V(r) = 1 4 πε o 2e 2 r 1 2e 2 r 2 + e 2 r 12 h 2 2m ( ) 2 1 + 2 2 Ψ + 1 4 πε o 2e 2 r 1 2e 2 r 2 + e 2 r 12 Ψ=ΕΨ 1 4 πε o e 2 r 12 —> 0 (1) –h 2 2m 2 1 2e 2 4 πε o r 1 Ψ+ –h 2 2m 2 2 2e 2 4 πε o r 2 Ψ=ΕΨ (2 29Ψ( r 1 , r 2 ) = Ψ 1 (r 1 ) Ψ 2 (r 2 ) where the one-electron wavefunctions are solutions to one-electron Schrödinger Eqns.: (3) –h 2 2m 2 1 2e 2 4 πε o r 1 Ψ 1 (r 1 ) 1 Ψ 1 (r 1 ) (4 29 –h 2 2m 2 2 2e 2 4 πε o r 2 Ψ 2 (r 2 ) 2 Ψ 2 (r 2 ) Note that 2 1 only operates on the coordinates of electron 1 2 1 Ψ 1 (r 1 ) Ψ 2 (r 2 ) = Ψ 2 (r 2
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