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Quantum particle on a surface: Catenary surface and Paraboloid of revolution
- Publication Year :
- 2021
-
Abstract
- We revisit the Schr\"{o}dinger equation of a quantum particle that is confined on a curved surface. Inspired by the novel work of R. C. T. da Costa [1] we find the field equation in a more convenient notation. The contribution of the principal curvatures in the effective binding potential on the surface is emphasized. Furthermore, using the so-called Monge-Gauge we construct the approximate Schr\"{o}dinger equation for a flat surface with small fluctuations. Finally, the resulting Schr\"{o}dinger equation is solved for some specific surfaces. In particular, we give exact solutions for a particle confined on a Catenary surface and a paraboloid of revolution.<br />Comment: 15 pages 17 figures
- Subjects :
- Physics
Surface (mathematics)
Paraboloid
Work (thermodynamics)
Quantum particle
Quantum Physics
FOS: Physical sciences
Condensed Matter Physics
Atomic and Molecular Physics, and Optics
Schrödinger equation
symbols.namesake
Classical mechanics
Catenary
symbols
Particle
Field equation
Quantum Physics (quant-ph)
Nonlinear Sciences::Pattern Formation and Solitons
Mathematical Physics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....0b0db5385d7b30eafcc88171e4dc1c79