## Gravitational Schrödinger Equation from Ginzburg-Landau Equation, and Its Noncommutative Spacetime Coordinate Representation

**Authors:** V. Christianto

Despite known analogy between condensed matter physics
and various cosmological phenomena, a neat linkage between
low-energy superfluid and celestial quantization is not yet
widely accepted in literature. In the present article we argue
that gravitational Schrödinger equation could be derived from
time-dependent Ginzburg-Landau (or Gross-Pitaevskii) that is
commonly used to describe superfluid dynamics. The solution
for celestial quantization takes the same form with Nottale
equation. Provided this proposed solution corresponds to the
facts, and then it could be used as alternative solution to
predict celestial orbits from quantized superfluid vortice
dynamics. Furthermore, we also discuss a representation of the
wavefunction solution using noncommutative spacetime
coordinate. Some implications of this solution were discussed
particularly in the context of offering a plausible explanation
of the physical origin of quantization of motion of celestial
objects.

**Comments:** recovered from sciprint.org

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### Submission history

[v1] 10 Mar 2007

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