Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9867189 | Annals of Physics | 2005 | 17 Pages |
Abstract
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincaré half plane (AdS2), de Sitter plane (dS2), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Physics and Astronomy (General)
Authors
Keivan Aghababaei Samani, Mina Zarei,