Anharmonic oscillators and the null bootstrap

TL;DR

This paper applies the perturbative null bootstrap method to compute energy levels and ladder operators for anharmonic oscillators, including non-Hermitian PT symmetric cases, confirming results with traditional perturbation theory.

Contribution

It introduces the null bootstrap approach for anharmonic oscillators and extends it to non-Hermitian PT symmetric Hamiltonians, providing a novel computational framework.

Findings

Bootstrap yields energy eigenvalues up to second order in coupling.

Results agree with traditional perturbation theory.

Extended method to PT symmetric non-Hermitian oscillators.

Abstract

We employ the technique of perturbative analytic null bootstrap to obtain the energy eigenvalues and ladder operators of the sextic anharmonic oscillator up to second order in the coupling. We confirm our results by deriving the same from traditional perturbation theory. We further perform the bootstrap approach on non-Hermitian PT symmetric Hamiltonians, focusing on the shifted harmonic oscillator and the celebrated cubic anharmonic oscillator.