Dynamical symmetry algebra for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. Selecting the starting point as a well-known factorization method of the Hamiltonian under consideration, we have found three basis elements of this algebra. The algebra defined through those basis elements is an su (1,1) Heisenberg–Lie algebra. Different special cases and the limit relations from the basis elements to the Heisenberg–Weyl algebra of the nonrelativistic quantum harmonic oscillator are discussed, too.

中文翻译：

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具有位置相关有效质量的半约束谐振子模型的动力学对称性

构造了具有位置相关有效质量的半约束谐振子模型的动力学对称代数。选择所考虑的哈密顿量的著名因式分解方法作为起点，我们发现了该代数的三个基本元素。通过这些基本元素定义的代数是 su (1,1) Heisenberg-Lie 代数。还讨论了不同的特殊情况以及从基本元素到非相对论量子谐振子的海森堡-韦尔代数的极限关系。