Spectrum of the Coulomb-plus-Yukawa potential by the method of potential envelopes

Abstract

The method of potential envelopes is used to analyse the bound-state spectrum of the Schrödinger Hamiltonian H = −Δ + V(r), where V(r) = −β/r + γe−λr/r, γ < β. It is established that upper or lower bounds to the eigenenergies Enl(β,γ,λ) are generated by the simple formula, [Formula: see text] where [Formula: see text] if γ < 0 and [Formula: see text] if γ > 0. The results are compared with eigenvalues computed numerically by a finite-element method and also with the results of a variational calculation.