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Optimization of kinetic energy of a micro-object by impulse fields

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Abstract

The generalization is performed of the Schrodinger equation for the kinetic energy of a micro-object to potential fields with the structure of distribution of the first order of singularity. This made it possible to solve the problem of minimization of the kinetic energy of a micro-object at the prescribed level of its observation in the class of potentials concentrated in a limited volume with a smooth surface. It was found that the singular component of the optimal potential is a simple layer concentrated at the volume boundary. Graphs are displayed of some affine transformations of the squares of optimal wave functions and appropriate potentials.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    D. S. Zavalishchin & S. T. Zavalishchin

Authors
  1. D. S. Zavalishchin
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  2. S. T. Zavalishchin
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Original Russian Text © D.S. Zavalishchin, S.T. Zavalishchin, 2007, published in Avtomatika i Telemekhanika, 2007, No. 10, pp. 28–37.

This work was supported by the Russian Foundation for Basic Research, project nos. 05-01-00434 and 06-01-00445.

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Zavalishchin, D.S., Zavalishchin, S.T. Optimization of kinetic energy of a micro-object by impulse fields. Autom Remote Control 68, 1756–1764 (2007). https://doi.org/10.1134/S0005117907100049

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  • DOI: https://doi.org/10.1134/S0005117907100049

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