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A finite difference method (FDM) applicable to a two dimensional (2D) quantumdot was developed as a non-conventional approach to the theoreticalunderstandings of quantum devices. This method can be applied to a realisticpotential with an arbitrary shape. Using this method, the Hamiltonian in atri-diagonal matrix could be obtained from any 2D potential, and theHamiltonian could be diagonalized numerically for the eigenvalues. Thelegitimacy of this method was first checked by comparing the results with afinite round well with the analytic solutions. Two truncated harmonic wellswere examined as a realistic model potential for lateral double quantum dots(DQDs) and for triple quantum dots (TQDs). The successful applications of the2D FDM were observed with the entanglements in the DQDs. The level-splittingand anticrossing behaviors of the DQDs could be obtained by varying thedistance between the dots and by introducing asymmetry in the well-depths. The2D FDM results for linear/triangular TQDs were compared with the tight bindingapproximations.

Finite difference method for the arbitrary potential in two dimensions: application to double/triple quantum dots