A note on "The Klein-Gordon oscillator in (1+2)-dimensions G\"urses space-time backgrounds (Ann. Phys. (N. Y.) 404 (2019) 1)"

TL;DR

This paper revisits the Klein-Gordon oscillator in (1+2)-dimensional G"urses space-time, clarifying the energy-dependent frequency and exploring its unique spectroscopic features within this curved background.

Contribution

It provides a detailed analysis of the KG-oscillator in G"urses space-time, emphasizing the energy-dependent frequency and uncovering novel spectroscopic properties.

Findings

Energy-dependent oscillator frequency derived

Spectroscopic features unique to G"urses space-time identified

Clarification and correction of previous results

Abstract

We revisit and discuss the KG-oscillator in the $(1+2)$-dimensional G\"{u}rses space-time studied in (F. Ahmed, Ann. Phys. (N. Y.) 404 (2019) 1). The modified oscillator frequency {\it i.e.,} $\tilde{\omega}^{2}=(\Omega^{2}\,E^{2}+\eta^{2})$ appeared in the eigenvalue equation is an energy-dependent parameter, and consequently, the results are accurately reported here. Moreover, we show some interesting spectroscopic features indulged within the very nature of G\"{u}rses space-time for the KG-G\"{u}rses oscillators.