Find Momentum Operators for 1s Electron in Hydrogen Atom

[leenaa]

Find < px >,< p > and < p2 > for the 1s electron ofa hydrogen atom.

i am tried the solution but momentum operators Differential for x or y or z and the wave equation depends on the r !

 

[fzero]

You need to use the transformation to spherical coordinates and the chain rule to compute the derivatives. Also, it's very likely that your textbook discusses the transformation of derivatives in Cartesian coordinates to derivatives in spherical coordinates, so you might find some useful formulas already derived for you.

 

[leenaa]

Thank you very much

http://img104.herosh.com/2010/11/18/211847127.jpg"


But the show of the integral of Sec[\[Theta]] does not converge on {0,2 \[Pi]}
Is this true!

 

[fzero]

You can't just determine $$\partial r/\partial x$$ by considering dx alone, since dr appears in the dy and dz equations as well. You can however compute

$$\frac{\partial r}{\partial x} = \frac{\partial }{\partial x} \sqrt{x^2 + y^2 + z^2} = \frac{x}{r}.$$

Therefore

$$\frac{\partial}{\partial x} = \sin\theta \cos \phi \frac{\partial}{\partial r} + \text{angular derivs}.$$

 

[leenaa]

Thank you very much
Clearer idea