Representations of the rotation group may be formulated in second-quantised language via Schwinger's transcription of angular momentum states onto states of an effective two-dimensional oscillator. In the case of the molecular asymmetric rigid rotor, by projecting onto the state space of rigid body rotations, the standard Ray Hamiltonian H(1, ¦Ê, -1) (with asymmetry parameter 1 ¡Ý ¦Ê ¡Ý -1), becomes a quadratic polynomial in the generators of the associated dynamical su(1, 1) algebra. We point out that H(1, ¦Ê, -1) is in fact quadratic in the Gaudin operators arising from the quasiclassical limit of an associated suq(1, 1) Yang-Baxter algebra. The general asymmetric rigid rotor Hamiltonian is thus an exactly solvable model. This fact has important implications for the structure of the spectrum, as well as for the eigenstates and correlation functions of the model.
History
Publication title
Molecular Physics
Volume
106
Issue
7
Pagination
955-961
ISSN
0026-8976
Department/School
School of Natural Sciences
Publisher
Taylor & Francis Ltd
Place of publication
England
Rights statement
The definitive published version is available online at: http://www.tandf.co.uk/journals