Second-Order Perturbation in Adaptive Perturbation Method

Abstract

The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all diagonal elements for a Fock state. We consider the harmonic oscillator with the interacting term, ${\lambda }_1{x}^4/6+{\lambda }_2{x}^6/120$, where ${\lambda }_1$ and ${\lambda }_2$ are coupling constants, and $x$ is the position operator. The spectrum shows a quantitative result from the second-order, less than 1 percent error, compared to a numerical solution when turning off the ${\lambda }_2$. When we turn on the ${\lambda }_2$, more deviation occurs, but the error is still less than 2 percent. We show a quantitative result beyond a weak-coupling region. Our study should provide interest in the holographic principle and strongly coupled boundary theory.

11 pages, 6 tables, minor changes, reference added

References in corpus (2)

• Parity Anomaly and Duality Web
• Adaptive Perturbation Method in Quantum Mechanics

Cited by in corpus (2)

• Accurate Study from Adaptive Perturbation Method
• The application of adaptive perturbation theory in strongly coupled double harmonic oscillator system