= Coulomb angular-momentum intertwining
{c}
{title2=$H_{l+1}A_l=A_lH_l$}
The Coulomb radial factors satisfy $[A_l,A_l^\dagger]=a^2(l+1)/r^2=ma^2(H_{l+1}-H_l)/\hbar^2$. 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.
Back to article page
