This article is cited in 1 paper

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Theoretical and Mathematical Physics

Problems with Laplace operator on topological surfaces

M. Y. Shalaginov^a, M. G. Ivanov^b, M. V. Dolgopolov<sup>c

a</sup> School of Electrical and Computer Engineering, Purdue University, West Lafayette, 47907 Indiana, USA
^b Dept. of Theoretical Physics, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region
^c Dept. of General and Theoretical Physics, Samara State University, Samara

Abstract: 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, quantization, Laplace operator, Mobius strip, Klein bottle, torus.

UDC: 517.954

MSC: 35R01

Original article submitted 20/XII/2010
revision submitted – 20/V/2011

DOI: 10.14498/vsgtu877

Bibliographic databases:

• 
• 
•