Abstract We derive the energy levels of a circular Quantum Dot (QD) under a transverse magnetic field, incorporating the Ben-Daniel Duke boundary condition (BDD). The parameters in our model are the confinement barrier height, the size of the QD, the magnetic field strength, and a mass ratio highlighting the effect of using BDD. Charge densities, transition energies, and the dependence of energies on magnetic field has been calculated to show the strong influence of BDD. We find that our numerical calculations agree well with experimental results on the GaAs-InGaAs Quantum Dot and can be used further. We also provide an insightful analytical approximation to our numerical results, which converges well for larger values of size and confinement.

中文翻译：

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使用 BenDaniel-Duke 边界条件对圆形量子点进行朗道量化

摘要 我们推导出横向磁场下圆形量子点 (QD) 的能级，并结合 Ben-Daniel Duke 边界条件 (BDD)。我们模型中的参数是限制势垒高度、QD 的大小、磁场强度和突出使用 BDD 效果的质量比。电荷密度、跃迁能和能量对磁场的依赖性已被计算，以显示 BDD 的强烈影响。我们发现我们的数值计算与 GaAs-InGaAs 量子点的实验结果非常吻合，可以进一步使用。我们还为我们的数值结果提供了一个有见地的分析近似，它对于较大的尺寸和限制值很好地收敛。