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VOL. 9 | 2008 From Deformed Surfaces with Prescribed Quantum Properties to New Two-Dimentional Quantum Devices


We propose a problem in differential geometry, i.e., which dformed surfaces produce prescribed curvature induced quantum potentials. We solve this inverse problem in the case of surfaces of revolution. We also show that there exist rotational surfaces in the form of a circular strip around the axis of symmetry which allow particles with generic angular momentum to bind. The quantum physics of a collection of circular strips of curved surfaces glued together is discussed in the conclusion in view of the possibility to engineer devices based on thin films.


Published: 1 January 2008
First available in Project Euclid: 13 July 2015

zbMATH: 1197.53121
MathSciNet: MR2436267

Digital Object Identifier: 10.7546/giq-9-2008-135-145

Rights: Copyright © 2008 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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