The quantum anharmonic oscillator in the Heisenberg picture and multiple scale techniques

TL;DR

This paper explores the application of multiple scale techniques to the quantum anharmonic oscillator within the Heisenberg picture, revealing new insights into its equations of motion and spectral properties.

Contribution

It introduces the use of multiple scale methods in quantum mechanics to analyze the anharmonic oscillator, highlighting novel features in its solution and spectrum.

Findings

Perturbation series free from resonant terms

Insights into Heisenberg equations of motion

New spectral features of the quantum anharmonic oscillator

Abstract

Multiple scale techniques are well-known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution of the Heisenberg equations of motion and the Hamiltonian spectrum.