Nonlinear Schroedinger-Poisson definition of fine-structure-constant's value ∼1/137

By numerically investigating the nonlinear Schroedinger-Poisson eigenstates of a condensed Bose gas of charged particles that is confined in a two-dimensional axisymmetric parabolic potential 1/2 meω2r2 (e.g. quantum-dot helium), it is shown that the probability amplitude between two nonlinear-and hence non-orthogonal-eigenstates displays an interference pattern scaled (within 0.03 %) by graphic equation Since α = e2/ h-bar c ∼ 1/137 is the fine structure constant, this stunning result-indeed velocity of light c does not enter the present non-relativistic model-is tentatively explained by the existence of a 'nonlinear' bound state of the trapped particle-particle interaction Coulomb field whose energy cal E = half pi hbar omega defines the induced emission or absorption equilibrium processes between two appropriate chemical potentials. Besides, a non-decoherence quantum-classical transition with increasing nonlinearity is pointed out. As a possible experimental test for the present theory, the 0s2 →1s2 nonlinear transition in an ℎ ω = 1.66meV GaAs quantum-dot helium is emphasized.