Hi, I have been trying to get the expression for the transition dipole moment of hydrogen but I am not able to get the expression. Hope someone can help me with that.(adsbygoogle = window.adsbygoogle || []).push({});

I want to evaluate [itex]\vec{d}(v)=<v|\hat{r}|0>[/itex] where v is the free state and 0 is the 1s wave function for hydrogen.

[itex]\vec{d}(v)=\int dτ\frac{\alpha^{3/4}}{\pi^{1/2}}exp(-\sqrt{\alpha}r)(-ih\frac{d}{dp})exp(-ipr)[/itex]

After integration by parts i got [itex]\frac{\alpha^{3/4}}{\pi^{1/2}}\left(\frac{1}{\sqrt{\alpha}+ip}\right)^{2}[/itex]

However, it should be [itex]\vec{d}(v)=i\left(\frac{2^{7/2}}{\pi}\alpha^{5/4}\right)\frac{p}{\left( p^2+\alpha\right)^3}[/itex].

Can someone point out where I went wrong?

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# Need help regarding transition dipole moment

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