Physics – Quantum Physics
Scientific paper
2006-11-21
Physics
Quantum Physics
21 pages, no figure. The first paper in our serial studies. Its earlier version is quant-ph/0602055
Scientific paper
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.
No associations
LandOfFree
Quantum mechanics in general quantum systems (I): Exact solution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum mechanics in general quantum systems (I): Exact solution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum mechanics in general quantum systems (I): Exact solution will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-339106