在本論文中，我們利用徑向的無限深位能阱來模擬利用自組裝法(self-assembled)所製造出的半導體量子單環與量子雙環。我們以量子單環的確切解為基底來展開量子單環和雙環中的電子或電洞的哈米頓（Hamiltonian）函數，再將其數值對角化求得本徵能量及本徵函數。我們發現在外加均勻磁場下，量子單及雙環皆存在AB效應(Aharonov-Bohm effect)。此外，我們也分別研究了在外加均勻磁場及自旋軌道交互作用下，電子與電洞之簡併能階因對稱性破壞造成的變化。我們亦研究了在自旋軌道交互作用之下，AB週期震盪行為的變化。

In this thesis, a model of radial infinite square well is considered to simulate the self-assembled semiconductor single quantum ring and double rings. By using the exact solutions of the single quantum ring, one can expand the Hamiltonian function of electron or hole in single quantum ring and double rings and obtain the eigen-energies and eigen-functions numerically. Aharonov-Bohm effect is found to exist in both of the two cases under the exterior uniform magnetic field. In addition, we also study the energy spectra in the presence of spin-orbit interaction. It is found that the periodic oscillation of AB effect can be degraded seriously by the spin-orbit interaction.

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