【作者】 肖艳萍；

【导师】 刘全慧；

【作者基本信息】 湖南大学 ， 理论物理， 2005， 硕士

【摘要】 微分几何中的曲面论,用两个变量就可以完全参数化一个二维曲面。也就是,当一个粒子约束在曲面上运动时,只需要两个独立的变量就可以完全刻划粒子的运动。但是,当我们从物理的角度审视这一问题时,就会发现可以把这个曲面嵌入一个三维空间中,粒子的运动可以在笛卡儿坐标下分解为三个互相正交的方向。动能算符T和三个笛卡儿动量Pi (i =1,2,3)的关系似乎为: 其中Pi (i =1,2,3)为厄密算符。事实上,这一关系的成立是有条件的:要么不存在约束,要么发生在经典极限下。在存在约束时,上式应代之以其中fi (i =1,2,3)是非平凡的函数。本文用圆环面,旋转抛物面,旋转单叶双曲面,磁场中的荷电平面转子,球面转子等体系中的量子运动说明函数fi(i =1,2,3)是存在的。在不同的矢势下,荷电粒子的力学动量从而动能的表达式是不同的。本文研究了它们之间和量子规范相因子的关系,发现规范相因子会自然出现在动能算符中。更多还原

【Abstract】 According to surface theory in differential geometry, the two-dimensional surface is parameterized by two variables. I. e., when a particle moves on the surface, only two variables suffice to describe the motion of the particle. However, when examining the same problem in the physical point of view, the motion of the particle can also be described in the three-dimensional coordinates. Explicitly, the relation between kinetic energy T and Hermitian Cartesian momentum Pi ( i=1,2,3)is speciously which holds either for the system being free of constraint or for the system in classical limit. Moreover, under constraint, above expression should be replaced by, where fi ( i=1,2,3)are the non-trivial functions. This paper utilizes quantum motions on the torus surface, paraboloid of revolution, hyperboloid of revolution of one sheet, charged planar and spherical rotator etc., to demonstrate the existence of the function f i. Since different vector potentials lead to different kinetic energies, the relationship between these kinetic energies and the gauge phase factors, is studied. Results show that the gauge phase factors can appear in the kinetic operator naturally.更多还原