The tunne1 current from a two-dimensional electron gas (2DΕG) into donor impurities in the quantum well of a double-barrier heterostructure is studied using the Bardeen Transfer-Hamiltonian formalism. Resonant tunnelling occurs when the donor level lies within the energy range of occupied 2DΕG states. It is shown that in the presence of a magnetic field Β normal to the current flow, the magnetocurrent J(B) is determined by the Fourier probability density of the donor wave function corresponding to the momentum p0 transferred to the tunnelling electrons by the Lorentz force. Then experimental J(B) curves, in principle, directly measure the donor wave function.The magnetocurrent is quenched when p0 greatly exceeds the width of the distribution of momentum Fourier components of the donor wave function.PACS numbers: 73.40. Gk, 71.55.Eq, 85.30.Τv The precision growth of semiconductor heterostructures has permitted systematic studies of a wide range of quantum phenomena. In particular, quantum interference and high-energy electron dynamics have been extensively investigated using double-barrier resonant-tunnelling structures (DBRTS) in which the electrons are injected from a twodimensional electron gas (2DEG) into the subband states of the quantum well. The injection energy is determined by the applied bias voltage. Using a transverse magnetic field (perpendicular to the current flow) to control the momentum of the injected carriers, the magnetotunnelling rates and lateral energy dispersion curves have been determined for electrons and holes [1][2][3].Recent experiments on laterally-gated DBRTS and on GaAs/(AlGa)As DBRTS containing an n-type δ-doped layer in the middle of the quantum well, have revealed resonances in the current-voltage curve below the threshold voltage for resonant tunnelling through the lowest subband minimum of the well [4,5]. These resonances are suppressed by a transverse magnetic field s: 10 T and originate from tunnelling through bound states of the donor impurities.We assume that the donors in the quantum well are essentially non-interacting since in the experiments, the nearest-neighbour separation greatly exceeds the (737)