We present a quantitative analysis of the energy levels and wave functions of carriers in a cubic quantum dot of GaAs embedded in Ga(1-x)AlxAs 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 Oh. 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.
Bharadwaj, S., Pandey, S., & Ram-Mohan, L. R. (2017). Removal of accidental degeneracy in semiconductor quantum dots. Physical Review B, 96(19). https://doi.org/10.1103/physrevb.96.195305
*denotes a WPI undergraduate student author