The Baute quantum time of arrival distribution in a uniform gravitational field and its classical limit

Abstract

Using the formalism of crossing states (A. Baute, R. Sala, J.P. Palao, J.G. Muga, I.L. Egusquiza Phys. Rev. A 61 (2000) 022118), we examine the time of arrival probability distribution of a freely falling quantum particle in a uniform gravitational field. For the case of a gaussian wave packet these time of arrival probability distributions are manifestly mass-dependent. However in the classical limit this massdependence becomes exponentially small, recovering the expected behavior.