Eur. Phys. J. Plus (2012) 127: 17
https://doi.org/10.1140/epjp/i2012-12017-y

Regular Article

Time-dependent trapping of a molecule

Department of Physics, University of Northern British Columbia, Prince George, V2N 4Z9, British Columbia, Canada

^* e-mail: mras@unbc.ca

Received: 17 August 2011
Accepted: 26 January 2012
Published online: 15 February 2012

Abstract

In this paper, we present a theoretical, time-dependent quantum mechanical study of a diatomic, homonuclear molecule subject to an external trapping potential. We choose a Gaussian wave packet to represent the wave function of the center of mass (c.m.) of the molecule, and calculate its propagation numerically using Crank-Nicholson integration. We consider different initial locations of the wave function of the c.m. of the molecule: inside the trapping potential, outside the trap, and partly inside and partly outside. We also examine for each initial location the motion for a range of initial speeds of the c.m. relative to the trap. We calculate the probability that the molecule ends up trapped inside the potential well as well as the probabilities that the molecule will escape the trap by tunneling past or reflecting off the trapping potential. We also reveal the intermediary behavior of the motion, including oscillations in time of the position of the c.m., especially near the edges of the trap, as well as oscillations between bound and unbound molecular states. We compare our results with real systems and experimental work on trapping of molecules at low temperatures.