## 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

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### Submission history

[v1] 6 Mar 2010

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