Transmission probability of electrons traversing two dimensional electron gas

We have calculated transmission probability of electrons injected via quantum point contacts into a two dimensional electron gas exposed to a small magnetic field. We have numerically solved the time-independent Schrodinger equation for a static magnetic field. Using the Green's function method with Dirichlet's boundary conditions it was possible to evaluate the wave function for a line at any distance from the injector. The extracted dimensions and amplitudes of the scattering centres correspond well with estimations from the first principle calculations on the correlation of remote donors in size and strength. From these results the information about the size, the energetic height of scattering potential was observed.