Verifying Eigen Solutions for H2 Molecule

[LagrangeEuler]

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

 

[DrDu]

No, what you get is a crude approximation (the Valence-Bond or Heitler-London wavefunction) for the spatial part of the true wavefunction.