Schrödinger spectrum generated by the Cornell potential

The eigenvalues $E_{n\ell}^d(a,c)$ of the $d$-dimensional Schrödinger equation with the Cornell potential $V(r)=-a/r+c\,r$, $a,c>0$ are analyzed by means of the envelope method and the asymptotic iteration method (AIM). Scaling arguments show that it is sufficient to know $E(1,λ)$, and the envelope method provides analytic bounds for the equivalent complete set of coupling functions $λ(E)$. Meanwhile the easily-implemented AIM procedure yields highly accurate numerical eigenvalues with little computational effort.

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