SQUARE-PRESERVING AND SYMPLECTIC STRUCTURE AND SCHEME FOR QUANTUM SYSTEM

The time-dependent Schrodinger equation is a square-preserving and sym plectic (SPS) transformation, The canonical equations of quantum syste ms are deduced by using eigenfunction expansion, The normal-square of wavefunction of the quantum systems is an invariant integral of the ca nonical equations and then the symplectic schemes that based on both C ayley transformation and diagonal Pade approximation to exp(x) are als o square-preserving, The evaluated example show that the SPS approach is reasonable and effective for solving time-evolution of quantum syst em.