Studies in Perturbation Theory .II. Generalization of the Brillouin-Wigner Formalism III, Solution of the Schrodinger Equation under a Variation of a Parameter

摘要

The solution of the schrodinger equation by means of the variation principle and a discrete basis leads to a certain secular equation. In a previous paper it was shown that, if this equation is handled by a partitioning technique, a generalization of the schrodinger-brillouin formula is obtained. The procedure contains an inverse matrix, and it is shown here that, if in the expression for the wave function this matrix is approximated to the m order, the corresponding matrix in the expectation value for the energy is approximated to order (2m+1). This gives a simple derivation and generalization of the Brillouin-wingner theorem. The connection between the variation principle and perturbation theory is further discussed.nThe solution of the chrodinger equation by means of the variation principle and discrete tut not necessarily orthonormal basis is studied in the case when the Hamiltonian is a function of a parameter. The coefficients in the power series expansions in of the wave function and the energy are explicitly determined in the form of expectation values, and the connection with the conventional schrodinger theory is discussed.