NEW APPROXIMATION TO THE BOUND-STATES OF SCHRODINGER-OPERATORS WITH COULOMB INTERACTION

In this work we present a mathematical formulation of the physical fac t that the bound states of a quantum system confined into a box Omega (with impenetrable walls) are similar to those of the unconfined syste m, if the box Omega is sufficiently large, and it is shown how the bou nd states of atomic and molecular Hamiltonians can be approximated by those of the system confined for a box Omega large enough (Dirichlet e igenproblem in Omega). Thus, a method for computing bound states is ob tained which has the advantage of reducing the problem to the case of compact operators. This implies that a broad class of numerical and an alytic techniques used for solving the Dirichlet problem, may be appli ed in full strength to obtain accurate computations of energy levels, wave functions, and other physical properties of interest. (C) 1994 Jo hn Wiley & Sons, Inc.