## Proceedings of the International Conference on Geometry, Integrability and Quantization

- Geom. Integrability & Quantization
- Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, ed. (Sofia: Softex, 2008), 135 - 145

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

Victor Atanasov and Rossen Dandoloff

#### 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.

#### Article information

**Dates**

First available in Project Euclid:
13 July 2015

**Permanent link to this document**

https://projecteuclid.org/
euclid.pgiq/1436793142

**Digital Object Identifier**

doi:10.7546/giq-9-2008-135-145

**Mathematical Reviews number (MathSciNet)**

MR2436267

**Zentralblatt MATH identifier**

1197.53121

#### Citation

Atanasov, Victor; Dandoloff, Rossen. From Deformed Surfaces with Prescribed Quantum Properties to New Two-Dimentional Quantum Devices. Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, 135--145, Softex, Sofia, Bulgaria, 2008. doi:10.7546/giq-9-2008-135-145. https://projecteuclid.org/euclid.pgiq/1436793142

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