$\Cal D$ -模理论中的子流形微分算子I：Schrodinger算子
Submanifold Differential Operators in $\Cal D$-Module Theory I : Schrödinger Operators
摘要：
在这四分之一个世纪里，嵌入或浸入实$n$维欧几里得空间$\EE^n$中的低维子流形中的微分算子已被作为量子力学模型进行研究，这些模型被实现为$\EE^n$中的算子对子流形的限制。在这十年中，Dirac算子的子流形已被调查，在这样的计划，这是确定与运营商的Frenet-Serret关系的空间曲线的情况下和广义Weierstrass关系的共形曲面的情况。这些狄拉克算子在微分几何中很受关注，因为它们完全表示子流形。在本系列和以后的系列文章中，我们将用$\DMod$ -模理论给出$\EE^n$中子流形上的微分算子的数学构造，并在数学上改写Dirac算子的最新结果.在这篇文章中，我们将在$\EE^n$中的低维子流形中建立薛定谔算子。
英文摘要：
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 $\EE^n$.
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