Abstract: The Symplectic algorithms for Hamiltonian mechanics initiated by K.Feng have proved to be a striking success. Since the underlying mathematics of Hamiltonian mechanics is sympledic geometry, the proper discretization should naturally keep the symplodic structure. We show that the Schrödinger equation, after suitable transformation, has a symplectic structure.Therefore the symplectic algorithms for Hamiltonian mechanics can be applied readily toquantum mechanics. As an example the evolution of a nuetron in a rotating magnetic field is calculated. The computational results show that the symplectic scheme is much better than the conventional one, especially for the case of long-term evolution.

Key words: symplectic algorithm, symplectic geometry, schrödinger equation