Studies On The Properties Of Confined Hydrogen Atom And Hydrogen Molecular Ion

External magnetic fields and external confined environment have a great e?ect onthe properties of atoms. The relational research work is one of the fundamental researchdirections of atomic physics and plays an important role in the comprehension the quan-tum quantum chaos, quantum size e?ect and shape e?ect. In addition, studying on theconfined atoms under quantum mechanics theory also has a great academical interest-ing, which get involved in the solving Schrodinger equation with inseparable variables,complicated boundary condition and interface condition. Meanwhile, there are intimaterelations between atomic physics and other fields such as astrophysics,condensed physics,plasma physics in studying the properties of atoms under external magnetic fields andconfined environment.In this paper, using the method of B-splines basis expansion, the diamagnetic spectraof hydrogen, the properties of hydrogen atom and the properties of hydrogen molecularion under di?erent confined potential have been studied. Some interesting results havebeen revealed. The major contents are as following:(i)For hydrogen atom under outside magnetic fields, the high accuracy diamagneticspectra of high Rydberg states with the energy range (?40cm?1,0) have been gotten.Comparisons with others results have shown that our methods are more e?cient thanthose of others. The statistical analysis of the high density Rydberg energy spectra havebeen studied, too.(ii)For hydrogen atom confined in infinity ellipsoidal cavity, the general rule of theground and low excited energies varying with the sizes and shapes of the confined ellip-soids have been discussed. The theoretical reasons of quantum size e?ects and quantumshape e?ects have also been analyzed.(iii)For hydrogenic-donor confined in spherical GaAs-Ga1?xAl xAs quantum dots,the e?ects of the size of quantum dots and thoses of di?erent o?-centre distance on theenergy spectra of hydrogenic-donor have been studied. With the help of partial-waveanalysis, a quantitative explanation about"abnormal"rules of the low-lying states of hydrogenic-donor for l = 0 states energies have been given.(iv)For hydrogen molecular ion-like impurity confined in spherical GaAs-Ga1?xAlxAs quantum dots, the change properties of energy spectra following the di?erent size ofquantum dots and nuclear distance have been studied. A feasible scheme to realize thecharge qubits by choosing suitable size of quantum dots and distance between nuclearshave been proposed.