H2 molecule

  • #1
653
15
Eigen - problem for atom ##1##
[tex](\frac{p^2_1}{2m}-\frac{e^2}{2\pi\epsilon_0r_{1a}})|\varphi_a^{(1)} \rangle=E_a|\varphi_a^{(1)}\rangle[/tex]
for atom ##2##
[tex](\frac{p^2_2}{2m}-\frac{e^2}{2\pi\epsilon_0r_{2b}})|\varphi_b^{(2)} \rangle=E_b|\varphi_b^{(2)}\rangle[/tex]
When I write
[tex]|q \rangle^{(\pm)}=\frac{1}{\sqrt{2}}(|\varphi_a^{(1)} \rangle|\varphi_b^{(2)}\rangle \pm |\varphi_a^{(2)} \rangle|\varphi_b^{(1)}\rangle)[/tex]
did I get the space part wavefunction of hydrogen molecule ##H_2##?
 

Answers and Replies

  • #2
DrDu
Science Advisor
6,144
817
No, what you get is a crude approximation (the Valence-Bond or Heitler-London wavefunction) for the spacial part of the true wavefunction.
 

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