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The nuclear Schrödinger equation can be approximately factored
into translational, rotational, and vibrational parts. McQuarrie
[1] explains how to do this for a diatomic in section
10-13. The rotational part can be cast into the form of the rigid
rotor model, and the vibrational part can be written as a system of
harmonic oscillators. Time does not allow further comment on the
nuclear Schrödinger equation, although it is central to molecular
spectroscopy.