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Some thoughts on a nonlinear Schrödinger equation motivated by information theory

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Abstract

The arguments leading to a nonlinear generalization of the Schrödinger equation in the context of the maximum uncertainty principle are reviewed. The exact and perturbative properties of that equation depend on a free regulating/interpolating parameter η, which can be fixed using energetics as is shown here. A linear theory with an external potential that reproduces some unusual exact solutions of the nonlinear equation is also discussed, together with possible symmetry enhancements in the nonlinear theory.

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Authors and Affiliations

  1. Department of Physics and University Scholars Programme, National University of Singapore, Kent Ridge, Singapore

    R. R. Parwani

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  1. R. R. Parwani
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 157–162, July, 2007.

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Parwani, R.R. Some thoughts on a nonlinear Schrödinger equation motivated by information theory. Theor Math Phys 152, 1012–1016 (2007). https://doi.org/10.1007/s11232-007-0085-1

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  • DOI: https://doi.org/10.1007/s11232-007-0085-1

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