  Starting from our idea of combining the Feynman path integral spirit and the
Dyson series kernel, we find an explicit and general form of time evolution
operator that is a $c$-number function and a power series of perturbation
including all order approximations in the unperturbed Hamiltonian
representation. Based on it, we obtain an exact solution of the Schr\"{o}dinger
equation in general quantum systems independent of time. Comparison of our
exact solution with the existed perturbation theory makes some features and
significance of our exact solution clear. The conclusions expressly indicate
that our exact solution is obviously consistent with the usual time-independent
perturbation theory at any order approximation, it explicitly calculates out
the expanding coefficients of the unperturbed state in the non-perturbation
method, and it fully solves the recurrence equation of the expansion
coefficients of final state in the unperturbed Hamiltonian representation from
a view of time-dependent perturbation theory. At the same time, the exact
solution of the von Neumann equation is also given. Our results can be thought
of as theoretical developments of quantum dynamics, and are helpful for
understanding the dynamical behavior and related subjects of general quantum
systems in both theory and application. Our exact solution, together with its
sequence studies on perturbation theory [An Min Wang, quant-ph/0611217] and
open system dynamics [An Min Wang, quant-ph/0601051] can be used to establish
the foundation of theoretical formulism of quantum mechanics in general quantum
systems. Further applications of our exact solution to quantum theory can be
expected.
