  We propose an improved scheme of perturbation theory based on our exact
solution [An Min Wang, quant-ph/0611216] in general quantum systems independent
of time. Our elementary start-point is to introduce the perturbing parameter as
late as possible. Our main skills are Hamiltonian redivision so as to overcome
a flaw of the usual perturbation theory, and the perturbing Hamiltonian matrix
product decomposition in order to separate the contraction and anti-contraction
terms. Our calculational technology is the limit process for eliminating
apparent divergences. Our central idea is ``dynamical rearrangement and
summation" for the sake of the partial contributions from the high order even
all order approximations absorbed in our perturbed solution. Consequently, we
obtain the improved forms of the zeroth, first, second and third order
perturbed solutions absorbing the partial contributions from the high order
even all order approximations of perturbation. Then we deduce the improved
transition probability. In special, we propose the revised Fermi's golden rule.
Moreover, we apply our scheme to obtain the improved forms of perturbed energy
and perturbed state. In addition, we study an easy understanding example of
two-state system to illustrate our scheme and show its advantages. All of this
implies the physical reasons and evidences why our improved scheme of
perturbation theory are actually calculable, operationally efficient,
conclusively more accurate. Our improved scheme is the further development and
interesting application of our exact solution, and it has been successfully
used to study on open system dynamics [An Min Wang, quant-ph/0601051].
