TY - JOUR

T1 - An action principle for complex quantum trajectories

AU - Poirier, Bill

AU - Tannor, David

N1 - Funding Information:
This work was supported by a grant from The Robert A. Welch Foundation (D-1523), and by a Small Grant for Exploratory Research from the National Science Foundation (CHE-0741321). Travel support from the US–Israel Binational Science Foundation (BSF-2008023) is also acknowledged. The authors also wish to express gratitude to Jeremy Schiff for many interesting and useful discussions related to the present work, and to Noa Zamstein for discovering the second-order equivalence of the BOMCA and BOMCA-like trajectories. One author (Poirier) also expresses gratitude for a Texas Tech University Faculty Development Leave, which has greatly facilitated this project.

PY - 2012/5/10

Y1 - 2012/5/10

N2 - In a recent paper [B. Poirier, Chem. Phys. 370, 4 (2010)], a formulation of quantum mechanics was presented for which the usual wavefunction and Schrdinger equation are replaced with an ensemble of real-valued trajectories satisfying a principle of least action. It was found that the resultant quantum trajectories are those of Bohmian mechanics. In this paper, analogous ideas are applied to Bohmian Mechanics with Complex Action (BOMCA). The standard BOMCA trajectories as previously defined are found not to satisfy an action principle. However, an alternate set of complex equations of motion is derived that does exhibit this desirable property, and an approximate numerical implementation is presented. Exact analytical results are also presented, for Gaussian wavepacket propagation under quadratic potentials.

AB - In a recent paper [B. Poirier, Chem. Phys. 370, 4 (2010)], a formulation of quantum mechanics was presented for which the usual wavefunction and Schrdinger equation are replaced with an ensemble of real-valued trajectories satisfying a principle of least action. It was found that the resultant quantum trajectories are those of Bohmian mechanics. In this paper, analogous ideas are applied to Bohmian Mechanics with Complex Action (BOMCA). The standard BOMCA trajectories as previously defined are found not to satisfy an action principle. However, an alternate set of complex equations of motion is derived that does exhibit this desirable property, and an approximate numerical implementation is presented. Exact analytical results are also presented, for Gaussian wavepacket propagation under quadratic potentials.

KW - complex trajectories

KW - principle of least action

KW - quantum mechanics

UR - http://www.scopus.com/inward/record.url?scp=84861889462&partnerID=8YFLogxK

U2 - 10.1080/00268976.2012.681811

DO - 10.1080/00268976.2012.681811

M3 - Article

AN - SCOPUS:84861889462

VL - 110

SP - 897

EP - 908

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 9-10

ER -