Schrödinger spectrum generated by the Cornell potential

Abstract

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

8 pages, 2 figures

References in corpus (1)

• Precise Numerical Solutions of Potential Problems Using Crank-Nicholson Method