Problems with Laplace operator on~topological~surfaces

M. Y. Shalaginov; M. G. Ivanov; M. V. Dolgopolov

Geodesic

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Problems with Laplace operator on~topological~surfaces

M. Y. Shalaginov ; M. G. Ivanov ; M. V. Dolgopolov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 243-250

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Résumé

This work highlights the problems related to the Laplace operator on topological surfaces such as Mobius strip, Klein bottle and torus. In particular, we discuss oscillations on the surface of the Mobius strip, eigenfunctions and eigenvalues of the Laplace operator on the surface of the Klein bottle, as well as behavior of a charged particle on the torus.

Keywords: quantum physics, non-Euclidean topological spaces, Laplace operator, Mobius strip, Klein bottle
Mots-clés : quantization, torus.

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M. Y. Shalaginov; M. G. Ivanov; M. V. Dolgopolov. Problems with Laplace operator on~topological~surfaces. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 243-250. http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a29/