Application of Connection in Molecular Dynamics

The evolution of electronic states in molecule has two origins: dynamical one produced by Schrödinger equation and kinematical one caused by base transformation due to nuclear motion. In current theories, the former gets analytic expression; the latter depends on heavy numerical calculation, which contains uncertainty. By using connection of fiber bundles, this paper establishes an analytic formula for the latter, and the numerical work is simplified. It shows the mathematical structure of molecule is fiber bundle. (paper)