SPECTRUM OF THE COULOMB-PLUS-YUKAWA POTENTIAL BY THE METHOD OF POTENTIAL ENVELOPES

The method of potential envelopes is used to analyse the bound-state spectrum of the Schrodinger Hamiltonian H = -DELTA + V(r), where V(r) = - beta/r + gamma-e(-lambda-r)/r, gamma < beta. It is established that upper or lower bounds to the eigenenergies E(nl)(beta, gamma, lambda) are generated by the simple formula, E(nl) almost-equal-to r > 0 min {(n + l)2/r2 + V(r)}, where almost-equal-to = less-than-or-equal-to if gamma < 0 and almost-equal-to = greater-than-or-equal-to if gamma > 0. The results are compared with eigenvalues computed numerically by a finite-element method and also with the results of a variational calculation.