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Proceedings of the Samahang Pisika ng Pilipinas

Quantum scattering of an exactly solvable anisotropic potential in paraboloidal coordinate systes

Philip Jordan D. Blancas, Eric A. Galapon

Published Oct 22, 2012• 0 citations
OpenAlex

Abstract

The differential scattering cross section of an anisotropic potential is computed by solving the time independent Schrodinger equation in paraboloidal coordinate system.

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Abstract We revisit the Schrödinger equation of a quantum particle that is confined on a curved surface. Inspired by the seminal work of da Costa (1980 Phys. Rev. A 23 1982) 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.