  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.
