论文标题
量子动力学中线性依赖的移动碱基的变异方法：应用于高斯函数
A variational approach for linearly dependent moving bases in quantum dynamics: application to Gaussian functions
论文作者
论文摘要
在本文中，我们介绍了线性依赖性的变异处理，以解决求解Schrödinger方程的非正交时间依赖性基础。该方法基于：i）线性独立的工作空间的定义，以及ii）在有限的时间步长上对传播器的变异结构。第二点允许该方法正确地说明沿时间演变的工作空间维度的变化。特别是，时间演变由半自动变换表示。测试以高斯基函数为基础的四分之一双孔电势进行，其中心根据经典运动方程而演变。我们表明，由此产生的动力学收敛到确切的动态，并且按构造统一。
In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schrödinger equation. The method is based on: i) the definition of a linearly independent working space, and ii) a variational construction of the propagator over finite time-steps. The second point allows the method to properly account for changes in the dimensionality of the working space along the time evolution. In particular, the time evolution is represented by a semi-unitary transformation. Tests are done on a quartic double-well potential with Gaussian basis function whose centers evolve according to classical equations of motion. We show that the resulting dynamics converges to the exact one and is unitary by construction.
