Submanifold Differential Operators in $\Cal D$-Module Theory I : Schrödinger Operators
| dc.creator | Matsutani, Shigeki | |
| dc.date | 1999-10-09 | |
| dc.date | 2000-01-09 | |
| dc.date.accessioned | 2026-07-07T05:31:07Z | |
| dc.date.available | 2026-07-07T05:31:07Z | |
| dc.description | For this quarter of century, differential operators in a lower dimensional submanifold embedded or immersed in real $n$-dimensional euclidean space $\EE^n$ have been studied as quantum mechanical models, which are realized as restriction of the operators in $\EE^n$ to the submanifold. For this decade, the Dirac operators in the submanifold have been investigated in such a scheme , which are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case. These Dirac operators are concerned well in the differential geometry, since they completely represent the submanifolds. In this and a future series of articles, we will give mathematical construction of the differential operators on a submanifold in $\EE^n$ in terms of $\DMod$-module theory and rewrite recent results of the Dirac operators mathematically. In this article, we will formulate Schrödinger operators in a low-dimensional submanifold in $\EE^n$. | |
| dc.description | AMS-Tex Use 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/9910051 | |
| dc.identifier | http://arxiv.org/abs/math/9910051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79225 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.title | Submanifold Differential Operators in $\Cal D$-Module Theory I : Schrödinger Operators | |
| dc.type | text |