Molecular Dissociation Model Boundary Value Problem

This paper studys the bound value problem of the model of molecular dissociation, we deduce the numerical calculation that the foundation goes forward in the theories. The chapter two introduces the theories which we use, mainly involving the molecular dynamics, the molecular potential energy function and molecular structures.The chapter three introduces some works which we do, mainly studying the potential energy function of triatomic molecules. This problem can be returned to the eigenfunction problem for the system whose energy is given. For a few of simple systems, we can get the analytic solution, but it is very difficult for the most systems, we use the numerical methods generally. We firstly discuss the one-dimensional system, and then mainly discuss two-dimensional system. We treat triatomic molecules ABC dissociating into products A+BC. We consider the linear model in which the diatomic fragment vibrates while its rotational degree of freedom is frozen. Important approximations and some numerical techniques are discussed in this paper. Although our work does not involve in a specific example, but we provide a good numerical method to discuss the potential energy function and structures of triatomic molecules, also putting forward some problems that don't be resolved yet, we need to study gradually in the future work.