By Volodimir Simulik

A suite of essays within which invited participants try and outline the character of the electron, the quantum particle that has defied characterization for almost a century.

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Orthonormality and equivalence are used 1 Ecore = = Ecore = ∫ N N ∫ 1 N N ∫ ∑ϖ d ′ ⎧ N ⎩ c =1 ∫ Ψ ⎪⎨⎪ ∑ω d ψ † ( xd ′ d ′ ′ c ⎧ ) ⎪⎨ ⎪ ⎩ ⎫ c ⎪ core Hˆ (c )ϖ ⎬⎪ Ψdx c ⎭ N ∑ω c ⎫ c ⎪ core Hˆ (c )ϖ ⎬ ⎪ ⎭ c =1 ∑ω ψ d ( xd ) dxc ⎡ a ρ (x ∫ ⎢∑ ε (x ) ρ (x ) ⎢⎣ i ψ 1 ( x1 ) Hˆ core (1)ψ 1 ( x1 ) dx1 = † d d i i = ε core ( x1 ) ρ1 ( x1 ) dx1 (formal definition) 2 i 1 core 1 1 1 1 )⎤ ⎥ ρ ( x ) dx ⎥⎦ 1 1 1 24 Jaime Keller For the electron-electron interaction (e-e), because the equivalence of the N electrons and using the expansion of the ψ, we obtain N ∑ϕ 2 Eint = e2 (1)α i∗ ∑ ϕ ∗j (2)α ∗j ∗ i i x12 j ∑ϕ (2)α k ∑ ϕl (1)α l dx1 dx 2 .

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