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Nonlinear Schroedinger Equations within the Nelson Quantization Picture

G. Kaniadakis·A. M. Scarfone
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Abstract

We present a class of nonlinear Schroedinger equations (NLSEs) describing, in the mean field approximation, systems of interacting particles. This class of NLSEs is obtained generalizing expediently the approach proposed in Ref. [G.K. Phys. Rev. A 55, 941 (1997)], where a classical system obeying to an exclusion-inclusion principle is quantized using the Nelson stochastic quantization. The new class of NLSEs is obtained starting from the most general nonlinear classical kinetics compatible with a constant diffusion coefficient D=\hbar/2m. Finally, in the case of s-stationary states, we propose a transformation which linearizes the NLSEs here proposed.

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G. Kaniadakis, A. M. Scarfone. 2003-03-18. Nonlinear Schroedinger Equations within the Nelson Quantization Picture. https://doi.org/10.1016/s0034-4877(03)80016-2

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