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The molecular asymmetric rigid rotor Hamiltonian as an exactly solvable model


Jarvis, PD and Yates, LA, The molecular asymmetric rigid rotor Hamiltonian as an exactly solvable model, Molecular Physics, 106, (7) pp. 955-961. ISSN 0026-8976 (2008) [Refereed Article]

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DOI: doi:10.1080/00268970802050394


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, 百, -1) (with asymmetry parameter 1 ≡ 百 ≡ -1), becomes a quadratic polynomial in the generators of the associated dynamical su(1, 1) algebra. We point out that H(1, 百, -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.

Item Details

Item Type:Refereed Article
Keywords:asymmetric rigid rotor; asymmetric top; molecular Hamiltonian; transfer matrix; exactly solvable model; Bethe <i>Ansatz</i>; quasi-classical limit; Gaudin operators
Research Division:Mathematical Sciences
Research Group:Mathematical physics
Research Field:Mathematical aspects of classical mechanics, quantum mechanics and quantum information theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
UTAS Author:Yates, LA (Dr Luke Yates)
ID Code:55474
Year Published:2008
Web of Science® Times Cited:1
Deposited By:Physics
Deposited On:2009-03-11
Last Modified:2015-02-07
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