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

摘要

The rotational invariance under the usual physical angular momentum of the su_q(2) Hamiltonian for the description of rotational 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 su_q(2) and use of q-deformed tensor products and q-deformed clebsch-Gordan coefficients. The rotational invariance of this su_q(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 the HF molecule are provided.