  The adaptive perturbation method decomposes a Hamiltonian by the diagonal
elements and non-diagonal elements of the Fock state. The diagonal elements of
the Fock state are solvable but can contain the information about coupling
constants. We study the harmonic oscillator with the interacting potential,
$\lambda_1x^4/6+\lambda_2x^6/120$, where $\lambda_1$ and $\lambda_2$ are
coupling constants, and $x$ is the position operator. In this study, each
perturbed term has an exact solution. We demonstrate the accurate study of the
spectrum and $\langle x^2\rangle$ up to the next leading-order correction. In
particular, we study a similar problem of Higgs field from the inverted mass
term to demonstrate the possible non-trivial application of particle physics.
