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

Man Kwong Mak, Chun Sing Leung, Tiberiu Harko

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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-A 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.

Original languageEnglish
Article number2150038
Pages (from-to)1-13
Number of pages13
JournalModern Physics Letters A
Issue number6
Publication statusPublished - 28 Feb 2021


  • Adomian Decomposition Method
  • dark energy
  • Schrödinger-Newton system
  • series solutions

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics
  • Physics and Astronomy(all)

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