Algebraic Solutions for the Asymmetric Rotor

Abstract

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 (D2) 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 half-integer.