中国物理B ›› 1999, Vol. 8 ›› Issue (1): 8-13.doi: 10.1088/1004-423X/8/1/002

• GENERAL • 上一篇    下一篇

VECTOR LADDER OPERATORS FOR THE CENTRAL POTENTIALS

倪致祥   

  1. Department of Physics, Fuyang Teachers College, Fuyang 236032, China
  • 收稿日期:1998-05-05 出版日期:1999-01-20 发布日期:1999-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No.19175016) and Education Commission of Anhui Province (Grant No. 97JL018), China.

VECTOR LADDER OPERATORS FOR THE CENTRAL POTENTIALS

Ni Zhi-xiang (倪致祥)   

  1. Department of Physics, Fuyang Teachers College, Fuyang 236032, China
  • Received:1998-05-05 Online:1999-01-20 Published:1999-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No.19175016) and Education Commission of Anhui Province (Grant No. 97JL018), China.

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摘要： 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.

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.

中图分类号:  (Algebraic methods)

  • 03.65.Fd
02.10.Ud (Linear algebra) 03.65.Ge (Solutions of wave equations: bound states)