Geometric Hamiltonian matrix on the analogy between geodesic equation and Schr\"{o}dinger equation
Mathematical Physics
2021-07-16 v1 math.MP
Abstract
By formally comparing the geodesic equation with the Schr\"{o}dinger equation on Riemannian manifold, we come up with the geometric Hamiltonian matrix on Riemannian manifold based on the geospin matrix, and we discuss its eigenvalue equation as well. Meanwhile, we get the geometric Hamiltonian function only related to the scalar curvature.
Keywords
Cite
@article{arxiv.2107.07288,
title = {Geometric Hamiltonian matrix on the analogy between geodesic equation and Schr\"{o}dinger equation},
author = {Jack Whongius},
journal= {arXiv preprint arXiv:2107.07288},
year = {2021}
}
Comments
6 pages. comments are welcome