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H2 molecule

  1. Aug 29, 2012 #1
    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##?
     
  2. jcsd
  3. Aug 29, 2012 #2

    DrDu

    User Avatar
    Science Advisor

    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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