A NONLINEAR IRREDUCIBLE FORM OF THE SCHRODINGER EQUATION FOR THE GROUND STATE OF THE SECOND-QUANTIZED HAMILTONIAN

摘要

The Schrodinger equation determining the second-quantized Hamiltonian ground state is considered. We state that it is useful to transform this equation through the exponential substitution of the type (7), (8), into nonlinear form (eq. (10) for the Hamiltonian (2-4)). The advantage achieved is that the coefficient functions of expan¬sion (8) are regular, unlike those, e.g., of another ground state representation (12), (13).nThis advantage is rather substantial for the following reasons:nIt implies the irreducibility of the coefficient functions C2n, r (8) in the sense of item 3.2;the representation (7), (8) turns out to be the simplest possible one. The ground state energy E0 is separated from the essential part of equations defining the coefficient functions;and it enters only the first of these equations. The excited states are defined by the con¬struction (15).