Integral to show selection rules

[georg gill]

Homework Statement

I am trying to calculate the selection rules from 2p to 1s. Above are the three results in (1152)-.(1154). And In the image one also finds the spherical harmonics factors. I can not determine which R and angular parts that give the three 2p waves. Can you show which ones that will create one of the 2p waves and integrate the radial (radius part) part of that integral?

Homework Equations

The image is taken from this site:
http://farside.ph.utexas.edu/teaching/qmech/Quantum/node122.html

The Attempt at a Solution

 

[DrClaude]

I can not determine which R and angular parts that give the three 2p waves.

What are the relevant quantum numbers?

 

[georg gill]

Homework Statement

View attachment 97566

I am trying to calculate the selection rules from 2p to 1s. Above are the three results in (1152)-.(1154). And In the image one also finds the spherical harmonics factors. I can not determine which R and angular parts that give the three 2p waves. Can you show which ones that will create one of the 2p waves and integrate the radial (radius part) part of that integral?

Homework Equations

The image is taken from this site:
http://farside.ph.utexas.edu/teaching/qmech/Quantum/node122.html

The Attempt at a Solution

https://www.physicsforums.com/attachments/97773

I get the right answer for the y comp except that I cn not get rid of the $$\pm$$. the answer for the y-comp is given in (1153).