Kinematic geometry of mass-triangles and reduction of Schrodinger's equation of three-body systems to partial differential equations solely defined on triangular parameters

Wu-Yi Hsiang

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Kinematic geometry of mass-triangles and reduction of Schrodinger's equation of three-body systems to partial differential equations solely defined on triangular parameters

机译：质量三角形的运动学几何并将三体系统的薛定inger方程简化为仅由三角形参数定义的偏微分方程

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Schrodinger's equation of a three-body sys- tem is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, R~9, naturally equipped with Jacobi's kinematic metric and with translational and rotational symmetries. The natural invariance of Schrod- inger's equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momen- tum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrodinger's equation to corresponding PDEs solely defined on triangular parameters--i.e., at the level of R~6/SO(3)-- has never been adequately treated.

机译：三体系统的薛定inger方程是在9维配置空间R〜9中定义的线性偏微分方程（PDE），自然配备有Jacobi运动学度量以及平移和旋转对称性。薛定inger方程相对于平移对称性的自然不变性使我们可以将构型空间减少到6维空间，而旋转对称性的结构空间则提供了角动量守恒的量子力学形式。但是，最大程度地利用旋转不变性以使我们能够将Schrodinger方程简化为仅在三角参数上定义的相应PDE的问题（即，在R〜6 / SO（3）的水平）从来没有充分解决过治疗。

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《Proceedings of the National Academy of Sciences of the United States of America》 |1997年第17期|p.8936-8938|共3页
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Wu-Yi Hsiang;
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收录信息美国《科学引文索引》(SCI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
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正文语种 eng
中图分类自然科学总论;
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Kinematic geometry of mass-triangles and reduction of Schrodinger's equation of three-body systems to partial differential equations solely defined on triangular parameters

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