Accurate Study from Adaptive Perturbation Method

Abstract

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, ${\lambda }_1{x}^4/6+{\lambda }_2{x}^6/120$, 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 $⟨x^2⟩$ 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.

arXiv comment19 pages, 8 tables, minor changes, reference added

References in corpus (5)

• Constraints on anomalous Higgs boson couplings using production and decay information in the four-lepton final state
• Parity Anomaly and Duality Web
• Adaptive Perturbation Theory: Quantum Mechanics and Field Theory
• Second-Order Perturbation in Adaptive Perturbation Method
• Adaptive Perturbation Method in Quantum Mechanics

Cited by in corpus (1)

• The application of adaptive perturbation theory in strongly coupled double harmonic oscillator system