1. The problem statement, all variables and given/known data Evaluate the matrix element <U210|z|U100> where by |Unlm> we mean the hydrogen atom orbital with it's quantum numbers. 2. Relevant equations 3. The attempt at a solution So where I'm getting stuck is on the integral, because the "U" portion of the wave function is given in terms of r and theta, whereas we are putting the z operator between these two U functions. So we get ∫U210(z)U100dz This is where I get stuck. I tried converting z to spherical coordinates, using z=r*cosθ, but then dz=cosθ dr - r*sinθdθ. Thus, when I integrate the radial portion, I still have θ unevaluated (still a variable) and vice versa. Then I tried converting r and θ to z and just integrating over dz. But when I put this integrand into Wolfram's online integral calculator, it seems too difficult to evaluate (and I wouldn't have any clue by hand). I'm wondering, is this even the correct method in the first place? It is just confusing to me to evaluate a 3-D hydrogen atom only along z. Usually the text I uses doesn't give impossible integrals, so I suspect I am setting it up incorrectly. To give some context, later in the problem, we are going to evaluate transition probabilities under perturbation theory, which also employs a z operator. Thank you!