Yangian In Quantum Transition In The Quantum Degenerate States Applications

Since C.N.Yang [1] and R.J.Baxter separately established Quantum Yang-Baxter Equation in 1960s, the investigations on quantum integrable models have been greatly promoted. Especially the theory of Yangian and quantum algebra theory that were established by V. G. Drinfeld offered a powerful mathematic method for the reach about the symmetry of quantum integrable models in physics. People have made great progress both in different kinds of realizations of Yangian and in the studies on quantum integrable models since 1992, and have given new physics understanding and theoretical results. For example, the Yangian symmetry and RTT integrablility of hydrogen atom had been reported at length.In this paper, we mainly apply the theory of Yangian to Quantum mechanics, studying the quantum transition of a quantum system with quantum degenerate states by means of Yangian Algebra. First, using a kind of realization of Yangian of a two angular momentum coupling system, we can work out the quantum states of the H = -S model, a two-lattice physics system whose orbital angular momentum and spin coupled in a special way. Then, we select that situation that a orbital angular momentum of any value coupled with another of the value of 1/2 as an example, discuss the degenerate states of the model. We try to find a realization{I,J} of Yangian of this system by using the Yangian symmetry we have found before, and try to construct the shift operators basedon {I,J} for degenerate states, as a result, we able to shift one degenerate state to another .Thus, it can be seen that we gained good results from Yangian. And Yangian connect the states with different weight factors, it is the extension of the operators in quantum mechanics.