*Review* **Fundamentals of Diatomic Molecular Spectroscopy**

**Christian G. Parigger**

> Physics and Astronomy Department, University of Tennessee, University of Tennessee Space Institute, Center for Laser Applications, 411 B.H. Goethert Parkway, Tullahoma, TN 37388-9700, USA; cparigge@tennessee.edu; Tel.: +1-(931)-841-5690

> **Abstract:** The interpretation of optical spectra requires thorough comprehension of quantum mechanics, especially understanding the concept of angular momentum operators. Suppose now that a transformation from laboratory-fixed to molecule-attached coordinates, by invoking the correspondence principle, induces reversed angular momentum operator identities. However, the foundations of quantum mechanics and the mathematical implementation of specific symmetries assert that reversal of motion or time reversal includes complex conjugation as part of anti-unitary operation. Quantum theory contraindicates sign changes of the fundamental angular momentum algebra. Reversed angular momentum sign changes are of a heuristic nature and are actually not needed in analysis of diatomic spectra. This review addresses sustenance of usual angular momentum theory, including presentation of straightforward proofs leading to falsification of the occurrence of reversed angular momentum identities. This review also summarizes aspects of a consistent implementation of quantum mechanics for spectroscopy with selected diatomic molecules of interest in astrophysics and in engineering applications.

> **Keywords:** foundations of quantum mechanics; molecular spectroscopy; diatomic molecules; symmetry transformations; optical emission spectroscopy; astrophysics

**Citation:** Parigger, C.G.

Fundamentals of Diatomic Molecular Spectroscopy. *Foundations* **2021**, *1*, 208–216. https://doi.org/10.3390/ foundations1020016

Academic Editor: Eugene Oks

Received: 19 September 2021 Accepted: 29 October 2021 Published: 2 November 2021

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