Study Of Yangian Eliminating Degenerate State Of Rb Atom

Quantum Yang-Baxter Equation is a successful theory that can relatively systemicallydispose of some nonlinear quantum integrable models. Especially the theory of Yangian andquantum algebra theory that were established by V.G.Drinfeld offered a powerful mathematicmethod for the reach about the symmetry of the integrable quantum mobudels in physics.Yangian algebra goes beyond Lie algebra in quantum mechanics. It can describe the new-stylesymmetry of one kind of model of nonlinear inaction. In addition, it can make up the shifting operator indifferent quantum states. People have made great progress both in different kinds of realizationsof Yangian and in the studies on quantum integrable models since 1992, and have given newphysics understanding and theoretical results. In this paper, we mainly apply the theory of Yangian algebra to a two angularmomentum coupling system, studying the quantum transition of a quantum system withquantum degenerate states, through the way of using Yangian operators. After getting theeigenvalues and the eigenvectors of Hamiltont: H₀ = -gL₁→·L₂→ + λL³₂ 。 We find theeigenvectors of this model are muti-degenerate states. In order to break up degenerate states,we construct the operator that is composed of Yangian operators, by which we can eliminatemuti-degenerate states in this system. Through the study of the question above, we will know the function Yangian operators intackling quantum transition. Furthermore we can better master the realization ofYangian algebra in physics. Yangian can connect the states with different weight factors, itis the extension of the operators in quantum mechanics.