## Numerical Solution of Time-Dependent Gravitational Schrödinger Equation

**Authors:** V. Christianto, Diego L. Rapoport, Florentin Smarandache

In recent years, there are attempts to describe quantization of planetary distance
based on time-independent gravitational Schrödinger equation, including Rubcic &
Rubcic's method and also Nottale's Scale Relativity method. Nonetheless, there is
no solution yet for time-dependent gravitational Schrödinger equation (TDGSE). In
the present paper, a numerical solution of time-dependent gravitational Schrödinger
equation is presented, apparently for the first time. This numerical solution leads
to gravitational Bohr-radius, as expected. In the subsequent section, we also discuss
plausible extension of this gravitational Schrödinger equation to include the effect
of phion condensate via Gross-Pitaevskii equation, as described recently by Moffat.
Alternatively one can consider this condensate from the viewpoint of Bogoliubov-deGennes
theory, which can be approximated with coupled time-independent
gravitational Schrödinger equation. Further observation is of course recommended
in order to refute or verify this proposition.

**Comments:** 5 pages

**Download:** **PDF**

### Submission history

[v1] 6 Mar 2010

**Unique-IP document downloads:** 127 times

**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.*

*
*