Path-integral analysis of arrival times with a complex potential
Abstract
A number of approaches to the arrival time problem employ a complex potential of a simple step function type and the arrival time distribution may then be calculated using the stationary scattering wave functions. Here, it is shown that in the Zeno limit (in which the potential becomes very large), the arrival time distribution may be obtained in a clear and simple way using a path integral representation of the propagator together with the path decomposition expansion (in which the propagator is factored across a surface of constant time). Crucially, this method shows that the resulting arrival time distribution, in the Zeno limit, is in fact independent of the form of the complex potential.
- Publication:
-
Physical Review A
- Pub Date:
- June 2008
- DOI:
- 10.1103/PhysRevA.77.062103
- arXiv:
- arXiv:0801.4308
- Bibcode:
- 2008PhRvA..77f2103H
- Keywords:
-
- 03.65.Xp;
- 03.65.Ta;
- Tunneling traversal time quantum Zeno dynamics;
- Foundations of quantum mechanics;
- measurement theory;
- Quantum Physics
- E-Print:
- 8 pages