## Exact Solutions of the Newton-Schroedinger Equation, Infinite Derivative Gravity and Schwarzschild Atoms

**Authors:** Carlos Castro

Exact solutions to the stationary spherically symmetric Newton-Schroedinger equation are proposed
in terms of integrals involving $generalized$ Gaussians. The energy eigenvalues are also obtained in terms of these integrals which agree with the numerical results in the literature. A discussion of infinite-derivative-gravity follows which allows to generalize the Newton-Schroedinger equation by $replacing$
the ordinary Poisson equation with a $modified$ non-local Poisson equation associated with infinite-derivative gravity. We proceed to replace the nonlinear Newton-Schroedinger equation for a non-linear quantum-like Bohm-Poisson equation involving Bohm's quantum potential, and where the fundamental quantity is $no$ longer the wave-function $ \Psi$ but the real-valued probability density $ \rho$. Finally, we discuss how the latter equations reflect a $nonlinear$ $feeding$ loop mechanism between matter and geometry which allows us to envisage a ``Schwarzschild atom" as a spherically symmetric probability cloud of matter which curves the geometry, and in turn, the geometry back-reacts on this matter cloud perturbing its initial distribution over the space, which in turn will affect the geometry, and so forth until static equilibrium is reached.

**Comments:** 14 Pages. submitted to Physics and Astronomy International Journal

**Download:** **PDF**

### Submission history

[v1] 2017-10-06 05:32:30

[v2] 2017-10-07 01:36:36

**Unique-IP document downloads:** 63 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*