论文标题
I.具有非智能主量子数的指数型轨道的完整和正顺序集
I. Complete and orthonormal sets of exponential-type orbitals with noninteger principal quantum numbers
论文作者
论文摘要
Slater型轨道的定义是普遍的。研究了与非授权主量子数的正顺序基函数与轨道轨道之间的转换。线性组合系数的分析表达式得出。为了测试公式的准确性，对非智能Slater型轨道进行了数值革兰氏式schmidt程序。实现了正交式轨道轨道的封闭式表达式。它用于概括Guseinov在[Int。 J. Quant。化学90，114（2002）]到主量子数的非全能值。 Riemann-Liouville型分数算子被认为是原子和分子物理中的使用。结果表明，在任意范围内，参数的正真实值的相对论分子辅助函数及其分析解决方案是天然的Riemann-Liouville型分数操作员。
The definition for the Slater-type orbitals is generalized. Transformation between an orthonormal basis function and the Slater-type orbital with non-integer principal quantum numbers is investigated. Analytical expressions for the linear combination coefficients are derived. In order to test the accuracy of the formulas, the numerical Gram-Schmidt procedure is performed for the non-integer Slater-type orbitals. A closed form expression for the orthogonalized Slater-type orbitals is achieved. It is used to generalize complete orthonormal sets of exponential-type orbitals obtained by Guseinov in [Int. J. Quant. Chem. 90, 114 (2002)] to non-integer values of principal quantum numbers. Riemann-Liouville type fractional calculus operators are considered to be use in atomic and molecular physics. It is shown that the relativistic molecular auxiliary functions and their analytical solutions for positive real values of parameters on arbitrary range are the natural Riemann-Liouville type fractional operators.
