(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An electron in a H atom occupies the combined spin and position state: R21{(sqrt(1/3)Y10χ+) + (sqrt(2/3)Y11χ-)} If you measured both the z component of spin and the distance from the origin, what is the probability density for finding the particle with spin up and at radius r?

2. Relevant equations

3. The attempt at a solution

The answer should just be |R21|^2*(1/3)*|Y10|^2*|χ+|^2 = (r^2)/(96πa^5) * exp(-r/a) * (cosθ)^2, right? Or do I need to do an integral? The theta dependence of my answer is bugging me, but I'm not entirely sure if I need to integrate over theta and phi to just get an r dependent answer? Could somebody please help me think through this? Thanks very much.

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# H atom electron in combined spin/position state

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