1. The problem statement, all variables and given/known data I've attached the question as a jpeg. I'm having trouble showing that the wavefunctions are orthonormal (i.e. Orthogonal and normal) When I try to show U_210 is normal I dont get 1: My working: ∫ |U_210|² = 1 I set the limits from 0 to infinity for the radial part and 0 to π for cos²θ , so: 1/(16πa^5) . ∫ (r² . exp(-r/a)) dr . ∫ cos²θ dθ = 1 I used the identity given in the question to integrate the radial part and I get 2a³ Then I integrate the cos²θ and I get π/2 Therefore, 1/(16πa^5) . 2a³ . π/2 = 1 (But of course this does not equal to 1, and I dont know what I'm doing wrong) Thanks very much.