Path integral quantization of certain noncentral systems with dynamical symmetries
Path integral quantization of certain noncentral systems with dynamical symmetries
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DOI：
10.1063/1.529244
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发表时间：
1991-07
影响因子：
1.3
通讯作者：
M. Carpio-Bernido
中科院分区：
文献类型：
--
作者：
M. Carpio-Bernido
路径积分量子化是针对五类势函数进行的，这些势函数出现在马卡罗夫、斯莫罗丁斯基、瓦利耶夫和温特尼茨[Nuovo Cimento A 52，1061（1967）]对具有动力学对称性的非相对论系统的系统搜索中。通过迭代应用贝特曼级数公式的极坐标路径积分，扩展的费曼内核或绿色的功能，无论是可能的，在超几何功能的极和方位角部分和径向路径积分的评估产生的能量本征值和归一化的波函数。特殊情况包括哈特曼势和环形振荡器。
Path integral quantization is done for the five classes of potentials appearing in the systematic search for nonrelativistic systems with dynamical symmetries done by Makarov, Smorodinsky, Valiev, and Winternitz [Nuovo Cimento A 52, 1061 (1967)]. By an iterated application of Bateman’s series formula to the polar coordinate path integral, an expansion is obtained of the Feynman kernel or the Green’s function, whichever is possible, in terms of hypergeometric functions of the polar and azimuthal parts and a radial path integral is obtained whose evaluation yields the energy eigenvalues and the normalized wave functions. Special cases include the Hartmann potential and the ring‐shaped oscillator.