论文标题
适用于时间依赖的schrödinger方程的精确五角核基质溶液
An Accurate Pentadiagonal Matrix Solution for the Time-Dependent Schrödinger Equation
论文作者
论文摘要
量子机械时间演化算子的统一形式之一是Cayley的近似。相同的数值实现涉及用三点公式在哈密顿量中替换第二个衍生物，从而导致线性方程的三角形系统。在这项工作中，我们调用了高度准确的五点模具，将波函数离散到隐式解释的五角核曲柄 - 尼古尔森方案上。证明所得解决方案比标准溶液明显准确。我们还讨论了双方波袋动力学的分辨率，并得出了从实验室角度来源的产品状态，从质量中心的角度来看，产品状态仍然是产品状态。这具有将复杂的两分动力学分解为两个独立的单粒子问题的深刻应用。
One of the unitary forms of the quantum mechanical time evolution operator is given by Cayley's approximation. A numerical implementation of the same involves the replacement of second derivatives in Hamiltonian with the three-point formula, which leads to a tridiagonal system of linear equations. In this work, we invoke the highly accurate five-point stencil to discretize the wave function onto an Implicit-Explicit pentadiagonal Crank-Nicolson scheme. It is demonstrated that the resultant solutions are significantly more accurate than the standard ones. We also discuss the resolution of bipartite wavepacket dynamics and derive conditions under which a product state from the laboratory perspective remains a product state from the center-of-mass point of view. This has profound applications for decoupling complicated bipartite dynamics into two independent single-particle problems.
