Quantum corrections to the classical time of arrival for linear potentials

Abstract

Using gaussian wavepackets, we investigate the expectation value < T > ofthe time of arrival operator T for a linear potential. An asymptotic series for < T > is obtained as  ℏ → 0, such that the zeroth order term reduces to the classical time of arrival. We interpret this asymptotic series for < T > as quantum correction terms to the classical time of arrival.