Analytic approximations to the energy eingenvalues of the quadratic Zeeman effect in two dimensions for hydrogenlike atoms

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Flavio, Citti^1 ; Enrique, Castro^2 ; Pablo, Martin^2,3 ; Luis, Cortés-Vega^4

Materials Engineering Department, Simón Bolivar University, Apartado 89000, Caracas

1080A, Venezuela^1

Physics Department, Simón Bolivar University, Apartado 89000, Caracas

1080A, Venezuela^2

Physics Department, Antofagasta University, Casilla 170, Antofagasta, Chile^3

Mathematics Department, Antofagasta University, Casilla 170, Antofagasta, Chile^4

关键词: Analytic approximation;    Auxiliary functions;    Bridge functions;    Energy eigenvalues;    Hydrogen-like atoms;    Multiple points;    Two-dimension;    Zeeman effect;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012105/pdf
DOI  :  10.1088/1742-6596/574/1/012105

来源: IOP

【 摘 要 】

Analytic energy eigenvalues approximations have been found for the 2-D quadratic Zeeman effect in hydrogenlike atoms. Here a new technique has been used, the so called multipoint quasirational technique (MPQA), which is an extension of the two-point quasirational approximation (TPQA) technique, previously used for the same problem. In our previous calculations, two expansions were used, one for small values of the magnetic field and other for large values, that is, expansions around zero and the infinity were determined. Later a bridge between both expansions was built using simple auxiliary functions as well as rational ones. In the present paper expansions around intermediate points were also determined, and used. In this way, the corresponding analytic bridge function is determined, taken care also of these new expansions, so the technique is a multiple point quasirational approximation (MPQA). The calculations are carried out for the ground state 1s and the excited states 2p-and 3d-, respectively. These results are now much better than those obtained in previous works.