Linear System of Differential Equations with a Quadratic Invariant as the Schrödinger Equation

Abstract Linear systems of differential equations with an invariant in the form a positive definite quadratic real Hilbert space are considered. It is assumed that system has simple spectrum and eigenvectors complete orthonormal system. Under these assumptions, linear can be represented Schrödinger equation by introducing suitable complex structure. As example, we present such representation for Maxwell without currents. In view observations, dynamics defined some partial treated terms basic principles methods quantum mechanics.