由於半導體量子點與環境材料中的界面可能存在著最低
能態，而使的受激發的電子與電洞被束縛在如球殼的界面
中，而非如球體的量子點中。我們分別計算了被束縛在球位
能與球殼位能障礙的中的電子與電洞在磁場中的能階，並由
此計算出其躍遷能量。我們發現在同樣的能量尺度下在球殼
位能中的能階與球位能中比起來彼此較為接近，且隨著磁場
上升的較快，這使得能階之間產生了非常多的交叉，同樣的
這些交叉也發生在躍遷能量中，有些交叉在球位能中並不容
易看到。我們也計算了其躍遷強度，並發現在球殼位能中能
量最低的幾個躍遷的躍遷強度會隨著磁場有先下降再稍微
上升到一個穩定值的現象，而在球位能中其躍遷強度只會下
降而趨近於一個穩定值。

It is possible that there exists some interface states with
lowest energy comparing to the energy states contributed by
quantum dot material and environment material, and thus the
electrons and holes might be confined in interface, which is a region of spherical shell, but not in quantum dot which is a region of ball. We calculated the energy levels of an electron or hole confined in a ball-like or shell-like potential barrier in magnetic field, and calculated their transition energies. We found that in same scale the energy levels in shell potential are closer to each other and increase with magnetic field faster than which in sphere potential, and therefore cause many crossings in
energy levels and in transition energies. Some crossings of
shell potential not appear in sphere potential in our computation. We also calculate the transition strength and found that, some strengths of lowest transition energies in shell potential will decrease rapidly and then a little increase to a terminal value with increasing magnetic field; in sphere potential the transition strengths of lowest energies only decrease and approximate to a terminal value when magnetic field increase.

Kittel, Introduction solid state physics (8th ed.). (Wiley, USA, 2005)
G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (5th ed.). (Harcourt, New York, 2001).
Richard L. Burden and J. Douglas Faires, Numerical Analysis (7th ed). (Brooks/Cole, US, 2001)
Stephen Gasiorowicz, Quantum Physics (3rd ed). (Wiley, USA, 2003)