Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2006-04-20
Nonlinear Sciences
Exactly Solvable and Integrable Systems
7 pages
Scientific paper
10.1088/0305-4470/39/20/L03
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum mechanical evolution will generally not have any stationary states. We look for conditions on the potential energy term such that the quantum mechanical evolution may possess stationary states without having to perform a continuum limit. When the stationary states are postulated to be solutions of a second-order ordinary differential equation (ODE) eigenvalue problem it is found that the potential is required to be a solution of a particular first-order ODE. Similarly, when the stationary states are postulated to be solutions of a second-order ordinary difference equation (O$\Delta$E) eigenvalue problem the potential is required to be a solution of a particular first-order O$\Delta$E. The classical limits (which are at times very nontrivial) are integrable maps.
Field Chris M.
Nijhoff Frank W.
No associations
LandOfFree
Time-sliced path integrals with stationary states 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 Time-sliced path integrals with stationary states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Time-sliced path integrals with stationary states will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-67196