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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Need help regarding transition dipole moment

**Physics Forums | Science Articles, Homework Help, Discussion**