Hartree product (orbital approximation) proof

[@lseinjr1]

(for *mobile* users)
00:29 Product wavefunction (separation of variables) Ψ₁(1)Ψ₂(2)
00:55 Separability of Hamiltonian operator H into H₁ and H₂
01:16 Ψ₁ as eigenfunction of H₁, Ψ₂ as eigenfunction of H₂
02:00 Full Hamiltonian acting on product wavefunction
03:32 Linearity of the Hamiltonian operator
04:19 Use facts that Ψ₁ and Ψ₂ are eigenfunctions of H₁ and H₂, with eigenvalues E₁ and E₂, respectively
05:16 Use commutativity of multiplication
05:50 Factor product wavefunction out of each term
06:05 Note that total (non-interacting) energy E is E₁ + E₂

[@maximebrohet4957]

Thank you kind sir, for saving my grades one hour before the exam

[@shimaalyasin4783]

well explained

[@MrGarry1410]

Thank you very much.

[@Blaisem]

Thank you! I was wondering how this came about. By the way, which step ignores electron-electron interactions (maybe you could denote by the color you used to draw the equation)? Are there maybe certain manipulations that would not have been permitted if electron-electron interactions were included?

[@Blaisem]

Ah nevermind, I figured it out. You wouldn't be able to separate the hamiltonian with electron-electron interaction, since the electron repulsion has a term depending on both electrons.

[@임덕필]

wow

[@SkanderTALEBHACINE]

Thanks