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outhsakotad
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Homework Statement
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?
Homework Equations
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.