Ma. Nunez et G. Izquierdo, NEW APPROXIMATION TO THE BOUND-STATES OF SCHRODINGER-OPERATORS WITH COULOMB INTERACTION, International journal of quantum chemistry, 1994, pp. 241-250
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.