Algebraic Solutions for the Asymmetric Rotor

摘要

Exact algebraic solutions for the energy eigenvalues and eigenstates of the asymmetric rotor are found using an infinite-dimensional algebraic method. The theory exploits a mapping from the Jordan-Schwinger realization of the SO(3)-SU(2) algebra to a complementary SU(1,1)structure.The Bethe ansatz solutions that emerge are shown to display the intrinsic Vierergruppe (D_2) symmetry of the rotor when the angular quantum number I is an integer, and the intrinsic quaternion group Q (i.e.,the double group D_2) symmetry when I is a halfinteger.