Converging lower bounds to atomic binding energies
Shailendra Singh · Journal of Mathematical Physics · 1981
A method is proposed to obtain approximations converging from below to a finite number of the nonrelativistic binding energies of atomic systems. The method requires that the Hamiltonian be decomposable as a sum of an unperturbed part and a non-negative perturbation. The eigenvalues of the unperturbed part are assumed to be known. For computational purposes, one needs the matrix elements of the square of the Hamiltonian, in addition to those of the Hamiltonian itself. These elements are used to construct a matrix valued function whose eigenvalues have the bounds as their fixed points. The elements of the matrix are obtained by solving a system of linear equations typical of variational methods. An iterative procedure is shown to yield converging lower bounds to the fixed points and thus to the binding energies.