dorsal/arxiv
View SchemaOn the geometric potential derived from Hermitian momenta on a curved surface
| Authors | M. Encinosa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508104 |
| URL | https://arxiv.org/abs/quant-ph/0508104 |
Abstract
A geometric potential $V_C$ depending on the mean and Gaussian curvatures of a surface $\Sigma$ arises when confining a particle initially in a three-dimensional space $\Omega$ onto $\Sigma$ when the particle Hamiltonian $H_\Omega$ is taken proportional to the Laplacian $L$ on $\Omega$. In this work rather than assume $H_\Omega \propto L$, momenta $P_\eta$ Hermitian over $\Omega$ are constructed and used to derive an alternate Hamiltonian $H_\eta$. The procedure leading to $V_C$, when performed with $H_\eta$, 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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"abstract": "A geometric potential $V_C$ depending on the mean and Gaussian curvatures of\na surface $\\Sigma$ arises when confining a particle initially in a\nthree-dimensional space $\\Omega$ onto $\\Sigma$ when the particle Hamiltonian\n$H_\\Omega$ is taken proportional to the Laplacian $L$ on $\\Omega$. In this work\nrather than assume $H_\\Omega \\propto L$, momenta $P_\\eta$ Hermitian over\n$\\Omega$ are constructed and used to derive an alternate Hamiltonian $H_\\eta$.\nThe procedure leading to $V_C$, when performed with $H_\\eta$, is shown to yield\n$V_C = 0$. To obtain a measure of the difference between the two approaches,\nnumerical results are presented for a toroidal model.",
"arxiv_id": "quant-ph/0508104",
"authors": [
"M. Encinosa"
],
"categories": [
"quant-ph"
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"title": "On the geometric potential derived from Hermitian momenta on a curved surface",
"url": "https://arxiv.org/abs/quant-ph/0508104"
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