Alternative analysis to perturbation theory

TL;DR

This paper introduces a new method in quantum mechanics that simplifies calculating energy corrections, wave functions, and system evolution, demonstrated on a perturbed harmonic oscillator.

Contribution

It presents an alternative to traditional perturbation theory, providing combined corrections and time evolution analysis in a single step, with a matrix form of Dyson series.

Findings

Successfully applied to harmonic oscillator example

Provides combined energy and wave function corrections

Derives a matrix form of Dyson series

Abstract

We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function, additionally we can analyze the time evolution of the system. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.