Universal Method of Modeling Linear Stationary Physical Fields

Abstract

The aim of this paper is to develop a method, described earlier, of solving quantum-mechanical problems into a universal numerical method of modeling fields of various physical nature. This method is based on reducing the initial equation of mathematical physics describing a given physical field to a simpler inhomogeneous equation with a known fundamental solution. This equation is then transformed into an inhomogeneous integral equation with a kernel expressed in terms of the known fundamental solution. The obtained integral equation with boundary conditions is solved numerically. To confirm the efficiency of the proposed numerical method, a two-dimensional and a three-dimensional boundary value problem with known solutions have been solved. Another important illustration of the efficiency of the proposed method is the solution of quantum-mechanical problems for one-dimensional and two-dimensional quantum oscillators. It is shown that the considered method allows one to find the energy eigenvalues and the eigenfunctions with acceptable accuracy.