Application of Polynomial su(2) Algebra to a Physical System with Symmetric Rosen-Morse Potential

10.6122/CJP.20150126A

Hong-Biao Zhang；San-Xing Guo

Chinese Journal of Physics

53卷2期（2015 / 04 / 01）

68 - 78

英文

A novel polynomial su(2) algebra is constructed in a physical system with the symmetric Rosen-Morse potential. Meanwhile, its specific representations are presented spontaneously. The polynomial su(2) algebra can be used as an algebraic technique to solve for the eigenvalues and eigenfunctions of the Hamiltonian with the symmetric Rosen-Morse potential (SRM). The output results from the mentioned algebraic approach allows us to explore the pair of raising and lowering operators Ĵ_± of the polynomial su(2) algebra as a pair of shift operators of our Hamiltonian. In addition, the usual su(2) algebra is obtained naturally from the polynomial su(2) algebra we built, also it reveals that the physical system with the SRM potential has a dynamical su(2) symmetry.