In this work we show the calculations of the infrared spectrum of donor impurities in semiconductor quantum wires in the presence of an axial magnetic field and a transversal electric field. We use the effective mass approximation and an extended variational technique for calculating simultaneously the ground and excited impurity states. In this approach we expand the envelope function in terms of a product of two restricted sets of radial and z-dependent basis of Gaussian functions, taking into account the reflection symmetry in planes perpendicular to the wire axis. The parameters of the Gaussian functions are fixed a priori to cover the relevant physical region and assure convergence. The energy spectrum of the impurity in the quantum wire is obtained by solving a linear set of coupled equations for the expansion coefficients. To study the far-infrared absorption of the impurity confined in the wire, we obtain the absorption coefficient for transitions from ground to excited impurity states in the dipolar approximation. We calculate the selection rules for the allowed intra-donor transitions for circularly polarized radiation. We show the results for the absorption coefficient as a function of the photon energy for several external field strengths, arbitrary impurity positions and different geometric wire confinements.
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