CONVERGENCE OF KOHN VARIATIONAL METHOD

A theorem about the convergence of the Kohn variational method in the case of s-wave single-particle scattering in a well-behaved potential is proved. We show that, provided we use enough expansion functions, the estimated value of the phase shift can be made as near as we please to the correct result for all E within a range (a, b) except for a set whose measure will approach zero. The expansion functions χi used must form a core, which means that the two sets of all finite linear combinations of (T ± i)χi must each be dense, where T is the kinetic energy operator. © 1969.