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arXiv · 1609.05581

Exact solution of the two-axis countertwisting Hamiltonian

Feng Pan·Yao-Zhong Zhang·Jerry P. Draayer
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Abstract

It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz equations of the problem is derived. It is shown that solutions of the Bethe ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials. The total number of the four sets of the zeros equals exactly to $2J+1$ for a given integer angular momentum quantum number $J$, which proves the completeness of the solutions. It is also shown that double degeneracy in level energies may also occur in the $J\rightarrow\infty$ limit for integer $J$ case except a unique non-degenerate level with zero excitation energy.

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Feng Pan, Yao-Zhong Zhang, Jerry P. Draayer. 2016-09-19. Exact solution of the two-axis countertwisting Hamiltonian. https://doi.org/10.1016/j.aop.2016.11.019

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