Quantum mechanics in general quantum systems (IV): Green operator and path integral

Abstract

We first rewrite the perturbation expansion of the time evolution operator [An Min Wang, quant-ph/0611216] in a form as concise as possible. Then we derive out the perturbation expansion of the time-dependent complete Green operator and prove that it is just the Fourier transformation of the Dyson equation. Moreover, we obtain the perturbation expansion of the complete transition amplitude in the Feynman path integral formulism, and give an integral expression that relates the complete transition amplitude with the unperturbed transition amplitude. Further applications of these results can be expected and will be investigated in the near future.