Operator-based derivation of symmetric molecular top wavefunctions

The symmetric top wavefunctions are important in the study of rotational transitions of rigid body-rotor molecules. Using an explicit construction of the position-space state (determined from the Euler angles) and the definite angular momentum states (determined from the total angular momentum and the projections in the lab and body-fixed frames), we provide an operator-based derivation of these wavefunctions that just uses abstract states and operators without the need to work in position space. This is a representation-independent way to construct the wavefunction, providing an alternative to more common differential equation approaches. As an example application, we illustrate how they can be used to calculate the linewidth of the pure rotational transitions in the asymmetric top water molecule.