Physics – Quantum Physics
Scientific paper
2005-08-14
Physics
Quantum Physics
6 pages, no figures
Scientific paper
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.
No associations
LandOfFree
On the geometric potential derived from Hermitian momenta on a curved surface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the geometric potential derived from Hermitian momenta on a curved surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the geometric potential derived from Hermitian momenta on a curved surface will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-138512