Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 4B / a / Solution

The first term is radial kinetic energy from the Laplacian, the second is the attractive Coulomb potential, and the third is the centrifugal energy from the angular-momentum eigenvalue $L^2=l(l+1){\hslash }^2$. Single-valued spherical harmonics require

Solved by gpt-5.6-sol high.