A molecule of hydrogen. We assume that the only possible states of(adsbygoogle = window.adsbygoogle || []).push({});

its two electrons (indistinguishable) are [tex] |A\uparrow\rangle,

|A\downarrow\rangle, |B\uparrow\rangle[/tex] and [tex]|B\downarrow\rangle[/tex]

(A=1s-orbital at atom A, B=1s-orbital at atom B).

Formulate the 6 basis functions using the four possible single

particle states above. (Don't forget the Pauli-principle!)

Here is my solution:

Total spin S=1 or 0.

[tex]|1,1\rangle=|A\uparrow\rangle|B\uparrow\rangle[/tex],

[tex]|1,0\rangle=\frac{1}{\sqrt{2}}(|A\uparrow\rangle|B\downarrow\rangle+|A\downarrow\rangle|B\uparrow\rangle)[/tex],

[tex]|1,-1\rangle=|A\downarrow\rangle|B\downarrow\rangle[/tex],

[tex]|0,0\rangle=\frac{1}{\sqrt{2}}(|A\uparrow\rangle|B\downarrow\rangle-|A\downarrow\rangle|B\uparrow\rangle)[/tex].

Are they basis functions? There should be 6 but I got only 4.

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# Homework Help: Molecule of hydrogen

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