Truncated Reaction Operators

The reaction operator formulation for the exact solution of the Schrodinger equation is used with a truncated basis set to obtain approximate solutions. The relationship between this truncated reaction operator formalism and the Rayleigh—Ritz variational method is emphasized and shown explicitly. The truncated reaction operator and its matrix elements are discussed in general; computed and discussed for a simple example, the helium atom, using a three‐membered basis set. It is shown that the reaction operator can be replaced by a function which we call the ``effective'' perturbation potential Veff. Approximations to Veff are computed for the ground state of helium. This function has fundamental significance and lends itself to accurate empiricism.