I have a particular normalized energy eigenstate equation of a hydrogen atom. I am asked to find the probability per unit volume of finding the electron at a specific point. The point is r=a_0, theta=pi/6, and phi=pi/3.
The Attempt at a Solution
I am finding information on this problem confusing. It seems that to calculate the probability I either square the eigenstate equation and plug in the point coordinates, or integrate the square of the eigenstate equation using the limits r=0..a_0, theta=0..pi/6, and phi=0..pi/3.
Integrating doesn't make much sense to me because it seems as though I will be left with a chunk of volume instead of a point. On the other hand, I am not sure how simply squaring the eigenstate equation and evaluating it at the point will yield probability per unit volume with out dividing by (4/3)*(pi)*(a_0)^3 after.
Are either of these methods correct? If not, could someone please point me towards the correct direction? Thanks.