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The stationary Wigner equation with inflow boundary conditions(BVP)has been wideley applied in numerical simulation of nano semiconductor devices.I will introduce our recent work on analysis of the mathematical properties of the BVP and then present a semi-discrete version of the Wigner equation and prove that the constructed numerical solution by using the Shannon-Whittaker interpolation formula converges to the solution of the continuous BVP as the velocity mesh size goes to zero.