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arXiv · 2107.05621

Quantum particle on a surface: Catenary surface and Paraboloid of revolution

S. Habib Mazharimousavi
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Abstract

We revisit the Schrödinger 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 Schrödinger equation for a flat surface with small fluctuations. Finally, the resulting Schrödinger 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.

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S. Habib Mazharimousavi. 2021-08-13. Quantum particle on a surface: Catenary surface and Paraboloid of revolution. https://doi.org/10.1088/1402-4896%2Fac326f

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