Mean-Field Methods for Time-Dependent Quantum Dynamics of Many-Atom Systems

Methods that can accurately describe the quantum dynamics of large molecular systems have many potential applications. Since numerical solution of the time-dependent Schrödinger equation is only possible for systems with very few atoms, approximate methods are essential. This paper describes the development of such methods for this challenging time-dependent many-body quantum mechanical problem. Specifically, we focus on the development of mean-field theories, to which Mark Ratner has contributed greatly over the years, such as the time-dependent self-consistent field method, mixed quantum–classical methods, and the classical separable potentials method. The advantages and limitations of the different variants of mean-field theories are highlighted. Recent developments, aimed at applying mean-field methods for large systems, and their applications are presented. Issues where further methodological advancement is desirable are discussed. Examining the tools available so far, and the recent progress, we conclude there are promising perspectives for future development of mean-field theories for quantum dynamics with applications to realistic systems in important chemical and physical processes.