Garashchuk Sophya, Rassolov Vitaly A
Department of Chemistry and Biochemistry, University of South Carolina, South Carolina 29208, USA.
J Chem Phys. 2004 Nov 8;121(18):8711-5. doi: 10.1063/1.1804177.
Dynamics of quantum trajectories provides an efficient framework for description of various quantum effects in large systems, but it is unstable near the wave function density nodes where the quantum potential becomes singular. A mixed coordinate space/polar representation of the wave function is used to circumvent this problem. The resulting modified trajectory dynamics associated with the polar representation is nonsingular and smooth. The interference structure and the nodes of the wave function density are described, in principle, exactly in the coordinate representation. The approximate version of this approach is consistent with the semiclassical linearized quantum force method [S. Garashchuk and V. A. Rassolov, J. Chem. Phys. 120, 1181 (2004)]. This approach is exact for general wave functions with the density nodes in a locally quadratic potential.
量子轨迹动力学为描述大系统中的各种量子效应提供了一个有效的框架，但在量子势变得奇异的波函数密度节点附近它是不稳定的。波函数的混合坐标空间/极坐标表示被用来规避这个问题。与极坐标表示相关的由此产生的修正轨迹动力学是非奇异且平滑的。原则上，波函数密度的干涉结构和节点在坐标表示中能被精确描述。这种方法的近似版本与半经典线性化量子力方法一致[S. 加拉舒克和V. A. 拉索洛夫，《化学物理杂志》120, 1181 (2004)]。对于在局部二次势中具有密度节点的一般波函数，这种方法是精确的。
