Mathematics – Differential Geometry
Scientific paper
1999-10-09
Mathematics
Differential Geometry
AMS-Tex Use 24 pages
Scientific paper
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 Schr\"odinger operators in a low-dimensional submanifold in $\EE^n$.
No associations
LandOfFree
Submanifold Differential Operators in $\Cal D$-Module Theory I : Schrödinger Operators 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 Submanifold Differential Operators in $\Cal D$-Module Theory I : Schrödinger Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Submanifold Differential Operators in $\Cal D$-Module Theory I : Schrödinger Operators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-654554