| Research on low-dimensional quantum structures of semiconductor is one of the hot topics in condensed-matter physics in recent years, thus a great lot of researches in theory and experiment have been carried out. This paper studies quantum rings (QRs), quantum dots (QDs), and their coupling systems, and effect of factors, e.g. the magnetic field, on their properties. This thesis consists of five chapters.In chapter 1, properties and applications of QRs, QDs, and their coupling systems, as well as their theory research methods are briefly introduced.In chapter 2, theory of an N-electron QR subjected to the magnetic field is improved. The theory points are as follows: adopting product-functions of eigenfunctions of a single-electron QR as basis functions, the schrodinger equation of the N-electron QR is solved directly, and the qualitative exact eigensolutions (the eigenenergies and eigenstates) are obtained. Body density-functions of QRs are defined.In chapter 3, the few-electron QRs containing 1 up to 6 electrons are studied. First, evolution of the low-lying state energy against magnetic field is obtained. Secondly, the (L0,S0) phase diagrams of the ground states are plotted. At last, the information of the electronic structures is extracted.In chapter 4, the effect of the factors, i.e. magnetic fields, impurities, and confined potentials, on energy spectra of low-lying states of a 2-dimensional few-electron QD is discussed. The (L0, S0) phase diagrams of the ground states are plotted. The diagrams indicate clearly synthesized effect of the magnetic fields, the impurities and confined potentials on the ground states. Furthermore, their influence on the electronic structure of the ground states is revealed. In chapter 5, it is clarified for the theory method that two-dimensional QR coupling systems, i.e. QR- QR systems and QR- QD systems, are calculated with B-spline functions as basis, and pointed out that QRs and QDs are their examples.
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