From Deformed Surfaces with Prescribed Quantum Properties to New Two-Dimentional Quantum Devices

Abstract

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.