Abstract
We present a quantitative analysis of the energy levels and wave functions of carriers in a cubic quantum dot of GaAs embedded in ${\mathrm{Ga}}_{(1\ensuremath{-}x)}{\mathrm{Al}}_{x}\mathrm{As}$ with finite confining potential barriers at their interfaces. The energy spectrum has substantially reduced degeneracies compared to the analytically determined energy levels of the infinite-barrier quantum box of the same dimensions. The level degeneracy of states has been explained by group representations of the point group ${O}_{h}$. Projection operators for the irreducible representations provide a way to obtain the linear combinations of the degenerate wave functions which form a basis set for the representations. Energy-level splittings in the presence of externally applied electric and magnetic fields are also studied.
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