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arXiv · 2012.08239

The effects of the dark energy on the static Schr\"{o}dinger-Newton system -- an Adomian Decomposition Method and Pad\'{e} approximants based approach

Man Kwong Mak·Chun Sing Leung·Tiberiu Harko
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Abstract

The Schr\"{o}dinger-Newton system is a nonlinear system obtained by coupling together the linear Schr\"{o}dinger 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 Schr\"{o}dinger-Newton system, by modifying the Poisson equation through the addition of a new term. The corresponding Schr\"{o}dinger-Newton-$\Lambda$ 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 Pad\'{e} 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.

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Man Kwong Mak, Chun Sing Leung, Tiberiu Harko. 2020-12-15. The effects of the dark energy on the static Schr\"{o}dinger-Newton system -- an Adomian Decomposition Method and Pad\'{e} approximants based approach. https://doi.org/10.1142/s0217732321500383

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