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

8 pages

References in corpus (3)

• Quantum arrival times and operator normalization
• Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival
• Quantum kinetic energy densities: An operational approach

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