Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of a Hamiltonian where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several nearby Hamiltonians are known, standard perturbation theory cannot simultaneously use all this knowledge to provide a better approximation. We derive a formula enabling such an approximation result, and provide numerical examples for which this method is more competitive than standard perturbation theory.

翻译：标准特征值问题摄动理论包括在哈密顿量邻近区域获取特征模态的近似值，其中已知对应的特征模态。然而，若已知若干邻近哈密顿量对应的特征模态，标准摄动理论无法同时利用所有这些信息提供更优近似。我们推导出能够实现此类近似结果的公式，并提供数值示例，表明该方法相比标准摄动理论更具竞争力。