Comment on the paper "Third-harmonic generation investigated by a short-range bottomless exponential potential well" by M. Hu, K. Guo, Q. Yu, Z. Zhang [Superlattices and Microstructures, 122 (2018) 538-547]
A.M. Ishkhanyan, G.G. Demirkhanyan

TL;DR
This paper critically examines and refutes the findings of a previous study on third-harmonic generation, highlighting significant errors in the original analysis of quantum solutions and wave functions.
Contribution
It provides a detailed critique revealing errors in the original paper's solutions to the Schrödinger equation and bound-state wave functions.
Findings
Identification of errors in the Schrödinger equation solutions
Demonstration of incorrect bound-state wave functions
Clarification of the correct quantum mechanical approach
Abstract
We have discovered several severe errors in the recent paper M. Hu, K. Guo, Q. Yu, Z. Zhang [Superlattices and Microstructures, 122 (2018) 538-547]. Specifically, we demonstrate that both the solution of the Schr\"odinger equation and the bound-state wave functions used in the paper are incorrect.
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