Comment on: "Development of the perturbation theory using polynomial solutions" J. Math. Phys. 60, 012103 (2019)

TL;DR

This comment clarifies and evaluates a perturbation method for polynomial solutions in quantum physics, highlighting its accuracy and limitations, especially for deep double-well potentials.

Contribution

It provides a clearer presentation of Maiz's perturbation approach and compares its accuracy, revealing cases where it yields exact results and where it deteriorates.

Findings

The method agrees with original results in most cases.

In one case, the method produces an exact solution.

The approach deteriorates for deep double-well potentials.

Abstract

The purpose of this comment is to present the perturbation approach proposed by Maiz J. Math. Phys. 60, 012103 (2019) in a clearer way. The results of our straightforward procedure agree with those obtained by that author except for one case in which we obtain the exact result while he obtained an approximate one. In addition to it, we show that for sufficiently deep double-well potentials the perturbation approach deteriorates considerably.