ON SOME RELATIONS TO WAVE-FUNCTIONS OF ONE-DIMENSIONAL SCHRODINGER-EQUATION

A model problem connected with the investigation of a 2n one-dimensional Fermion system in a nonhomogeneous well with infinitely high walls is considered in this paper. The one-particle density rho(x) is supposed to be known. We show that in terms of rho(x) and the potential nu(x) without using the Schrodinger equation there may be found wave functions and one-particle energy levels appropriate to the density rho(x). An integro-differential equation satisfied by the functions nu(x) and rho(x) is obtained. The problem of satisfying N, nu-representability by a nonnegative function rho(x) is reduced to the problem of finding conditions for the existence of a solution of a certain equation.