Application of quantum self-frictional nonperturbative theory for the study of atomic anharmonic oscillator potentials and their arbitrary derivatives

Abstract

The self-frictional (SF) nonperturbative theory, introduced by one of the authors, is used for the evaluation of the $$V^{{(p_{l}^{ * } )}}$$ and $$V^{(\alpha^{ * })}$$ atomic anharmonic oscillator potentials and their derivatives, where $$p_{l}^{*} = 2l + 2 - \alpha^{ * }$$ and $$\alpha^{ * }$$ represent the integer $$(\alpha^{ * } = \alpha ,\; - \infty < \alpha \le 2$$ ) or non-integer ( $$\alpha^{ * } \ne \alpha ,\,\,\, - \infty < \alpha^{ * } < 3$$ ) SF quantum numbers. This study is based on the use of complete sets of $$\text{L}_{{}}^{{\left( {p_{l}^{*}} \right)}}$$ and $$\text{L}_{{}}^{{\left( {\alpha^{ * }} \right)}}$$ SF polynomials. The dependence of the potentials and their derivatives from the nucleus distances is investigated. All of the obtained results are valid for the arbitrary values of quantum numbers, scaling parameters and SF quantum numbers.