Reliability of high‐order phase‐integral eigenvalues for single and double minimum potentials
Reliability of high‐order phase‐integral eigenvalues for single and double minimum potentials
复制标题
单极和双极小势的高阶相位积分特征值的可靠性
DOI：
10.1063/1.446316
复制
发表时间：
1983
影响因子：
4.4
通讯作者：
R. J. Roy
中科院分区：
文献类型：
--
作者：
R. Paulsson;F. Karlsson;R. J. Roy
对于单最小模型势和双最小模型势，使用Froman和Froman相位积分近似计算能量本征值，并与精确（数值）量子力学结果进行比较。对于双最小势，结果可以从包括势垒最大值（σ项）附近的量子效应的正确相位积分量子化条件直到并包括5阶近似，以及从忽略σ项的量子化条件直到并包括13阶近似得到。当包含σ项时，三阶和五阶本征值对于所有实际目的来说都足够精确，甚至接近势垒最大值，但是如果忽略σ项，相位积分量子化条件在势垒最大值附近破裂，并且这种破裂随着阶数的增加而变得更加剧烈。这个性质被用来讨论相位积分近似的阶数将给出最佳结果的问题。对于单个最小LJ（.
For single and double minimum model potentials, energy eigenvalues are calculated using the Froman and Froman phase‐integral approximations and compared with exact (numerical) quantum mechanical results. For the double minimum potential, results are obtained both from the correct phase‐integral quantization condition including quantum effects near the barrier maximum (the σ term) up to and including the fifth‐order approximation, and from the quantization condition with the σ term neglected up to and including the 13th‐order approximation. When the σ term is included, the third‐ and fifth‐order eigenvalues are accurate enough for all practical purposes, even close to the barrier maximum, but if the σ term is neglected, the phase‐integral quantization condition breaks down near the barrier maximum, and this breakdown becomes more dramatic with increasing order. This property is used to discuss the question of which order of phase‐integral approximation will give the optimum result. For a single minimum LJ(...