= Bound-state ladder termination by norm positivity
{title2=$\|A_l\psi_E\|^2=ma^2E/\hbar^2+1/[2(l+1)^2]$}
For a normalized bound eigenstate of a factorized Coulomb radial <Hamiltonian>, the displayed squared norm must be nonnegative. At fixed negative $E$, increasing $l$ indefinitely would make it negative. The intertwining chain must therefore terminate with zero norm, giving $E=-\hbar^2/[2ma^2(L+1)^2]$. The positivity contradiction does not apply to the positive-energy continuum; domain preservation and normalizability are necessary assumptions.
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