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Kratzer potential algebraic representation and matrix elements recurrence formulae

机译:Kratzer势代数表示和矩阵元素递推公式

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Generalized recurrence relations for the calculation of multipole matrix elements for Kratzer potential wave functions are obtained operationally. These formulas have been determined by using a non-analytical procedure based on the algebraic representation of the Kratzer eigenfunctions along with the usual ladder properties and commutation relations. For that, the creation and annihilation operators are adequately derived by means of an alternative approach to the factorization method and the exact expressions for matrix elements are achieved with the aid of a relationship between the ladder operators associated with the bra and the ket. The proposed algebraic approach as well as the formulas for the calculation of matrix elements thus derived are quite simple and direct when compared with other alternative expressions already obtained analytically or pseudo-algebraically by means of the hypervirial theorem commutator algebra.
机译:可操作地获得用于计算Kratzer势波函数的多极矩阵元素的广义递推关系。这些公式是通过基于Kratzer本征函数的代数表示以及通常的梯形性质和换向关系使用非分析方法确定的。为此,通过对因式分解方法的另一种选择,可以充分地推导创建和an灭运算符,并借助与胸罩和ket相关的梯形运算符之间的关系获得矩阵元素的精确表达式。与通过超病毒定理换向子代数已经通过解析或伪代数方式获得的其他替代表达式相比,所提出的代数方法以及由此得出的矩阵元素的计算公式非常简单直接。

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