On the geometric potential derived from Hermitian momenta on a curved surface

2005/08/14 by M. Encinosa, Encinosa, M.
Physics and Astronomy · #FOS: Physical sciences #Nuclear physics research studies #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0508104

6 pages, no figures

arxiv created 2005/08/14 · openalex publication_date 2005/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A geometric potential V_C depending on the mean and Gaussian curvatures of a surface Σ arises when confining a particle initially in a three-dimensional space Ω onto Σ when the particle Hamiltonian H_Ω is taken proportional to the Laplacian L on Ω. In this work rather than assume H_Ω∝ L, momenta P_η Hermitian over Ω are constructed and used to derive an alternate Hamiltonian H_η. The procedure leading to V_C, when performed with H_η, is shown to yield V_C = 0. To obtain a measure of the difference between the two approaches, numerical results are presented for a toroidal model.

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