 Coulomb angular-momentum intertwining

The Coulomb radial factors satisfy $[A_l,A_l^{†}]=a^2(l+1)/r^2=m{a}^2(H_{l+1}-H_l)/{\hslash }^2$. Commuting $A_l$ through its factorized Hamiltonian gives the displayed intertwining relation. A nonzero transformed radial eigenfunction has the same energy in the next angular-momentum sector; this changes the radial sector, rather than being the usual magnetic-quantum-number raising operator within a fixed $l$ multiplet.