Abstract A new class of nonlinear Lie algebra has been found, which is generated naturally by the Hamiltonian operator, the square of the angular momentum operator and the ladder operator for the central potentials. According to the theory of nonlinear Lie algebra, without using the factorization method, we obtained the vector ladder operators for the three-dimensional isotropic harmonic oscillator and hydrogen atom. The radial components of these operators, which are independent of the quantum numbers, are just the radial ladder operators for the same potentials.
Fund: Project supported by the National Natural Science Foundation of China (Grant No.19175016) and Education Commission of Anhui Province (Grant No. 97JL018), China.
Cite this article:
Ni Zhi-xiang (倪致祥) VECTOR LADDER OPERATORS FOR THE CENTRAL POTENTIALS 1999 Acta Physica Sinica (Overseas Edition) 8 8
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