- #1
LagrangeEuler
- 711
- 22
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##?
(\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##?
