A two-dimensional Thomas–Fermi–Dirac–von Weizsacker formalism is derived using a local density approximation to study ballistic transport in quantum structures. The effective potential of the two-dimensional system is calculated by minimizing the energy using a conjugate gradient technique. This method enables us to study the effects of exchange and correlation, in addition to the direct Coulomb interaction, on quantum transport. We have applied this method to calculate the transport property of a T-shaped two-dimensional quantum wire in the presence of the effective potential.
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Wang et al. (1994) studied this question.