Accurate study from adaptive perturbation method

The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and nondiagonal of Fock state. state are solvable but can contain information about coupling constants. We study harmonic oscillator with interacting potential, [Formula: see text], where text] constants, is position operator. In this study, each perturbed term has an exact solution. demonstrate accurate spectrum up to next leading-order correction. particular, we similar problem Higgs field from inverted mass possible nontrivial application particle physics.