Schrödinger spectrum generated by the Cornell potential

Abstract

The eigenvalues Ednl (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 suffcient 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.

Keywords

• quarkonium
• quark-antiquark bound states
• confining potentials
• schrödinger’s equation
• asymptotic iteration method
• airy functions
• 03.65.ge
• 12.39.pn
• 11.10.qr
• 12.40.qq
• 14.40.gx
• 14.40.jz