Chou Chia-Chun, Wyatt Robert E
Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, TX 78712, USA.
J Chem Phys. 2008 Apr 21;128(15):154106. doi: 10.1063/1.2850743.
One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems.
在量子哈密顿-雅可比形式体系的框架下研究一维与时间无关的散射问题。推导了量子动量函数驻点附近局部近似量子轨迹的方程，并且量子动量函数的一阶导数与量子轨迹的局部结构相关。通过对运动方程进行数值积分，确定了两个例子的精确复量子轨迹。对于软势垒阶跃，一些粒子穿透到非经典区域，然后返回反射区域。对于势垒散射问题，量子轨迹可能在势垒区域螺旋进入吸引子或从排斥子中出来。尽管扩展到复空间的经典势对于每个问题都显示出不同的极点结构，但量子势在反射区域呈现相同的二阶极点结构。本文不仅分析了这些例子的复量子轨迹和总势，还展示了一维与时间无关散射问题的复量子轨迹和量子势的一般性质及相似结构。
Zotero 插件