Energy levels of an anharmonic oscillator in both weak and strong coupling limit using convergency of Morse-Feshbach non-linear perturbation series

TL;DR

This paper rigorously investigates the convergence of Morse-Feshbach nonlinear perturbation series to accurately determine energy levels of anharmonic oscillators across weak and strong coupling regimes, introducing a multi-step optimal splitting method.

Contribution

It introduces a new multi-step optimal splitting technique to ensure convergence of MFNPS for both ground and excited states of anharmonic oscillators.

Findings

Two-step optimal splitting suffices for ground state convergence.

Modified parameters are needed for excited states based on their dependency.

The method effectively computes energy levels in various coupling regimes.

Abstract

We make an extensive rigorous study on convergent behaviour of Morse-Feshbach nonlinear perturbation series (MFNPS) to find out energy levels of the anharmonic oscillator (AHO) in both weak and strong coupling limit. We develop a new method of multi step optimal splitting in order to get convergency in MFNPS for ground state of AHO and found that two step optimal splitting is sufficient to provide convergency in MFNPS. Unlike the ground state the optimal splitting parameters for excited states is modified according to their dependency on state in order to achieve convergency in MFNPS.