Suppose I have a wavefunction(adsbygoogle = window.adsbygoogle || []).push({});

ψ(r_{1}, r_{2})= (∅1s(r_{1}) ∅1p(r_{2}) - ∅1s(r_{2}) ∅1p(r_{1}))

And I know that ∅1s(r_{1}) and ∅1p(r_{1}) are normalized. How would I go about finding the normalization constant for ψ(r_{1}, r_{2})?

Everywhere I look just whips out a [itex]\frac{1}{\sqrt{2}}[/itex] out of nowhere:

http://en.wikipedia.org/wiki/Slater_determinant

http://farside.ph.utexas.edu/teaching/qmech/lectures/node59.html

http://vergil.chemistry.gatech.edu/notes/intro_estruc/intro_estruc.pdf

Are a few examples

A few of those seem to mention something about orthonormal orbitals, but their definition seems to rely on Dirac notation, which I'm not that familiar with. That also means it was infuriating to find this other thread https://www.physicsforums.com/showthread.php?t=178292, that looks like would've really helped me had I understood what the second poster said.

Currently I'm exactly where the first poster is, with

[itex]\frac{1}{N²}[/itex] = [itex]\int[/itex](∅1s(r_{1}) ∅1p(r_{2}) - 2 [itex]\int[/itex] ∅1s(r_{1}) ∅1p(r_{2}) ∅1s(r_{2}) ∅1p(r_{1}) + [itex]\int[/itex] ∅1p(r_{2}) ∅1s(r_{2}

As I mentioned, I think I know that the first and third terms must equal 1 for some reason, and the middle one equal 0, but I don't exactly know why. Any help?

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# Normalization constant for orbital wave functions

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