Eur. Phys. J. B (2018) 91: 97
https://doi.org/10.1140/epjb/e2018-90113-x

Regular Article

Time-dependent electron momenta from Born-Oppenheimer calculations^★

Universität Würzburg, Institut für Physikalische und Theoretische Chemie, Emil-Fischer-Str. 42, 97074 Würzburg, Germany

^a e-mail: voen@phys-chemie.uni-wuerzburg.de

Received: 1 March 2018
Received in final form: 10 April 2018
Published online: 4 June 2018

Abstract

The time-dependent expectation value of the electron momentum is zero if determined within the Born-Oppenheimer (BO) approximation. We show that one arrives at non-zero values, if the mean momentum is calculated from the time-derivative of the electronic coordinate. This is illustrated for the case of a coupled electron-nuclear motion in a one-dimensional model system. Regarding a situation where the BO approximation is valid, we find that the BO results are in perfect agreement with those derived from the numerically exact calculations. This holds for cases where the involved wave packets are well localized and also if a large spreading of the probability density occurs.