Summation over Feynman Histories in Polar Coordinates
Summation over Feynman Histories in Polar Coordinates
复制标题
极坐标中费曼历史的总结
DOI：
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发表时间：
1969
期刊：
影响因子：
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通讯作者：
A. Inomata
中科院分区：
文献类型：
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作者：
D. Peak;A. Inomata
使用极坐标检查在执行求和所有费曼的历史。在有心力问题中，拉格朗日路径积分和哈密顿路径积分的几个关系式被推导出来。应用程序是谐振子，均匀磁场中的带电粒子，平方反比势中的粒子和刚性转子。路径积分中从笛卡尔坐标到极坐标的变换与普通微积分中的变换有很大的不同，这使得极坐标路径积分的计算变得复杂。然而，据观察，对于中心对称的系统，使用极往往优于笛卡尔。
Use of polar coordinates is examined in performing summation over all Feynman histories. Several relationships for the Lagrangian path integral and the Hamiltonian path integral are derived in the central‐force problem. Applications are made for a harmonic oscillator, a charged particle in a uniform magnetic field, a particle in an inverse‐square potential, and a rigid rotator. Transformations from Cartesian to polar coordinates in path integrals are rather different from those in ordinary calculus and this complicates evaluation of path integrals in polars. However, it is observed that for systems of central symmetry use of polars is often advantageous over Cartesians.