In the presence of a non-local potential arising from electron-electron interaction, the conventional definition of current density J(c) = (e/2m)([(p - eA)psi]*psi -psi*[(p - eA)psi]) cannot satisfy the condition of current conservation, i.e., del. Jc not equal 0 in the steady state. In order to solve this problem, we give a new definition of current density including the contribution due to the non-local potential. We show that the current calculated based on the new definition of current density conserves the current and is the same as that obtained from the Landauer-Buttiker formula. Examples are given to demonstrate our results.
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