Applications Of B-spline Basis In Atomic Physics And The Artificial Confined Structures

B-spline functions are a set of piecewise polynomials, defined in a finite region, with the characters of high localizability, quasi-completeness, high flexibility. With these unique advances, B-spline basis set can be used to describe the bound states and continuous states well, and have wide applications in the field of atomic structure calculations, collision dy-namics, and the studies on the external field effects of atoms and molecules. In this thesis, B-spline basis method is applied to the studies on the precision energy spectra and the exter-nal field effects of simple atomic systems. A new kind of B-spline basis set with the periodic boundary condition is constructed and applied to the study on the energy spectra, the effects of the external magnetic field and impurities of quantum rings. The content of this thesis includes:(1) Using B-spline basis set method, the precise norelativistic and relativistic energy levels, wavefunctions, electric dipole polatizabilities and hyperpolarizabilities of hydrogen atoms are calculated. The magic wavelengths of the 1sâ†'2s and 1sâ†'3s transitions are iden-tified with high precision. A experimental scheme is proposed to use the laser at 1371 nm, which is one of the magic wavelengths of the 1sâ†'3s transition, to trap the hydrogen atom-s. This proposal is expected to be helpful to improve the accuracy of the lsâ†'3s transition frequency measurement.(2) A finite field method based on B-spline basis set and model potentials is developed. Using this method, the polarizabilities and hyperpolarizabilities of the low-energy states in Be+, Mg+, Ca+, and Sr+are calculated. The results provide the theoretical references for the analysis of the high-order polarization effects on the transition frequency shift. The hyperpolarization effects on the transition frequency shift for Ca+in the optical dipole trap are estimated by using quasi-electrostatic approximation.(3) Bethe logarithm is essential to the leading term of quantum electrodymanics (QED) corrections. In this thesis, Bethe logarithm of hydrogen atom is calculated using B-spline basis methd in three different gauges, the length, velocity and acceleration gauges. These calculations are independent on the results obtained by others and the self-consistent verifi-cation on our results. An effective computational procedure is developed to calculate Bethe logarithm with the existence of the external electric field, which laid the foundations for the calculations on the QED corrections of the polarizability.(4) A circle B-spline basis set is constructed for the expansion of the wavefunctions of the electron in quantum ring. This special construction of the B-spline basis can avoid the discontinuation of the derivatives in the traditional B-spline method on the two ends of the defined region. This new kind of B-spline basis set is applied to the study on the energy spectra, the effects of the external magnetic field and the impurities of the artificial confined structures, such as quantum rings.