Numerical implementation of Einstein-Brillouin-Keller quantization for arbitrary potentials
Numerical implementation of Einstein-Brillouin-Keller quantization for arbitrary potentials
复制标题
任意势的爱因斯坦-布里渊-凯勒量子化的数值实现
DOI：
10.1119/1.2192788
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
L. J. Curtis
中科院分区：
文献类型：
--
作者：
A. Larkoski;D. Ellis;L. J. Curtis
利用Einstein-Brillouin-Keller（EBK）量子化方程确定具有任意中心势的两体系统的能级，该中心势允许束缚态。这种处理是基于守恒定律，避免了牛顿和薛定谔微分方程。由于能级的解析解一般不存在，因此使用Newton-Raphson方法应用EBK条件并计算径向概率密度。适当的双原子分子的潜力被认为是和角动量的径向分布的影响，经典轨道的性质，和封闭轨道的可能性进行了研究。
The Einstein-Brillouin-Keller (EBK) quantization equation is used to determine the energy levels of a two-body system with an arbitrary central potential that allows for bound states. The treatment is based on the conservation laws and avoids both the Newtonian and Schrodinger differential equations. Because analytic solutions for the energy levels do not exist in general, the EBK condition is applied using the Newton-Raphson method and the radial probability density is computed. Potentials appropriate for a diatomic molecule are considered and the effect of the angular momentum on the radial distribution, the nature of the classical orbits, and the possibility of closed orbits is studied.