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Molecular Spectra from Rotationally Invariant Hamiltonians Based on the Quantum Algebra SUq(2) and Irreducible Tensor Operators under SUq(2)

Dennis Bonatsos·B. A. Kotsos·P. P. Raychev·P. A. Terziev
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Abstract

The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational molecular spectra is explicitly proved and a connection of this Hamiltonian to the formalism of Amal'sky is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITOs) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved and a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced. Numerical tests against an experimental rotational band of HF are provided.

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Dennis Bonatsos, B. A. Kotsos, P. P. Raychev, P. A. Terziev. 2003-11-27. Molecular Spectra from Rotationally Invariant Hamiltonians Based on the Quantum Algebra SUq(2) and Irreducible Tensor Operators under SUq(2). https://arxiv.org/abs/quant-ph/0311190

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