The effects of the dark energy on the static Schrödinger–Newton system — An Adomian Decomposition Method and Padé approximants based approach

Author:

Mak Man Kwong1,Leung Chun Sing2,Harko Tiberiu345

Affiliation:

1. Departamento de Física, Facultad de Ciencias Naturales, Universidad de Atacama, Copayapu 485, Copiapó, Chile

2. Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, Hong Kong S.A.R., P. R. China

3. Astronomical Observatory, 19 Ciresilor Street, 400487 Cluj-Napoca, Romania

4. Department of Physics, Babes-Bolyai University, Kogalniceanu Street, Cluj-Napoca 400084, Romania

5. School of Physics, Sun Yat-Sen University, Guangzhou 510275, P. R. China

Abstract

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 this 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-[Formula: see text] 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 exact numerical solution, and the effects of the dark energy on the structure of the Newtonian quantum system are fully investigated.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics

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