Path Integral Analysis of Arrival Times with a Complex Potential

TL;DR

This paper introduces a path integral approach to analyze arrival times in quantum mechanics using complex potentials, providing a clear method in the Zeno limit and for various potentials.

Contribution

It presents a novel path integral method for calculating arrival time distributions with complex potentials, simplifying the analysis in the Zeno limit.

Findings

Arrival time distribution can be derived using path integrals in the Zeno limit.

The method applies to a wide class of complex potentials.

The approach simplifies the calculation of arrival times in quantum systems.

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). This method also shows that the same result is obtained for a wide class of complex potentials.