The adaptive perturbation chooses a non-standard decomposition. The Hamiltonian becomes a sum of solvable and perturbation parts. We calculate the spectrum using the adaptive perturbation method at the leading-order to compare to numerical solutions. The maximum deviation is around 5% for different coupling regions. A perturbation study relies on whether a choice of leading-order is suitable. Our result with different parameters should show that the adaptive perturbation method provides appropriate saddle points to all coupling regions. In the end, we show that the perturbation parameters should not be a coupling constant.

中文翻译：

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量子力学中的自适应微扰方法

自适应扰动选择非标准分解。哈密​​顿量变成了可解部分和微扰部分的总和。我们使用领先阶的自适应扰动方法计算频谱，以与数值解进行比较。不同耦合区域的最大偏差约为 5%。扰动研究依赖于选择的前导顺序是否合适。我们使用不同参数的结果应该表明自适应扰动方法为所有耦合区域提供了适当的鞍点。最后，我们表明扰动参数不应该是耦合常数。