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
SN - 0026-8976
VL - 110
SP - 897
EP - 908
JO - Molecular Physics
JF - Molecular Physics
IS - 9-10
ER -