THE STABILITY OF MICROSCOPIC PARTICLES DESCRIBED BY THE NONLINEAR SCHRÖDINGER EQUATION

Abstract

A nonlinear Schrodinger equation is used to replace the linear Schrodinger equation in quantum mechanics and to study further the stability of microscopic particles by using the minimum theorem of energy and variational theorem. The investigation shows that the microscopic particles described by the nonlinear Shrodinger equation are localized and have a wave–corpuscle duality, which are completely different from that depicted by the linear Schrodinger equation in quantum mechanics. The results obtained by the minimum theorem of energy and variational theorem indicate that the solutions of the nonlinear Schrodinger equation or the microscopic particles are stable. Therefore, the microscopic particles have the feature of classical particles in such a case.