论文标题
暗能量对静态Schrödinger-Newton系统的影响 - 一种Adomian分解方法和基于Padé的方法
The effects of the dark energy on the static Schrödinger-Newton system -- an Adomian Decomposition Method and Padé approximants based approach
论文作者
论文摘要
Schrödinger-Newton系统是一种非线性系统，该系统通过将量子力学的线性schrödinger方程与牛顿力学的泊松方程相连。在目前的工作中，我们将通过通过添加新术语来修改泊松方程来研究宇宙常数（暗能量或真空波动）对Schrödinger-Newton系统的影响。相应的Schrödinger-Newton- $λ$系统无法准确解决，因此，对于其研究，必须求助于数值或半分析方法。为了获得系统的半分析解决方案，我们应用了Adomian分解方法，这是一种非常强大的方法，用于求解大型的非线性普通和部分微分方程。此外，通过使用padé近似值，将Adomian系列转化为有理功能。将半分析近似与完整的数值溶液进行了比较，并详细研究了暗能量对牛顿量子系统结构的影响。
The Schrödinger-Newton system is a nonlinear system obtained by coupling together the linear Schrödinger equation of quantum mechanics with the Poisson equation of Newtonian mechanics. In the present work we will investigate the effects of a cosmological constant (dark energy or vacuum fluctuation) on the Schrödinger-Newton system, by modifying the Poisson equation through the addition of a new term. The corresponding Schrödinger-Newton-$Λ$ system cannot be solved exactly, and therefore for its study one must resort to either numerical or semianalytical methods. In order to obtain a semianalytical solution of the system we apply the Adomian Decomposition Method, a very powerful method used for solving a large class of nonlinear ordinary and partial differential equations. Moreover, the Adomian series are transformed into rational functions by using the Padé approximants. The semianalytical approximation is compared with the full numerical solution, and the effects of the dark energy on the structure of the Newtonian quantum system are investigated in detail.
