A geometric setting for internal motions of the quantum three-body system
A geometric setting for internal motions of the quantum three-body system
复制标题
量子三体系统内部运动的几何设置
DOI：
--
复制
发表时间：
1987
期刊：
影响因子：
--
通讯作者：
T. Iwai
中科院分区：
文献类型：
--
作者：
T. Iwai
三体系统内部运动的量子力学是在复矢量丛理论的基础上建立起来的。三体系统在玻恩-奥本海默近似中被称为三原子分子。分子的内部状态被描述为由总角动量算子的平方的特征值指定的复向量束中的横截面。该丛具有线性连接，这是所谓的埃卡特条件的几何解释的自然结果。根据这种联系自然可以理解内部运动与旋转的耦合。获得了内部哈密顿算子，其中包括内部运动-旋转耦合和离心势。三原子分子的复向量丛被证明是一个平凡丛，尽管内部运动的几何设置与该丛是否平凡无关。
Quantum mechanics for internal motions of the three‐body system is set up on the basis of the complex vector bundle theory. The three‐body system is called a triatomic molecule in the Born–Oppenheimer approximation. The internal states of the molecule are described as cross sections in the complex vector bundle assigned by an eigenvalue of the square of the total angular momentum operator. This bundle is equipped with a linear connection, which is a natural consequence of a geometric interpretation of the so‐called Eckart condition. The coupling of the internal motion with the rotation is understood naturally in terms of this connection. The internal Hamiltonian operator is obtained which includes the internal motion–rotation coupling and a centrifugal potential. The complex vector bundle for the triatomic molecule proves to be a trivial bundle, though the geometric setting for the internal motion is independent of whether the bundle is trivial or not.