Hydrogenic impurity in a coaxial quantum well wire: Effect of different masses of wires and barriers

A variational calculation is given within the effective mass approximation of the binding energy of an axial or an off-axial impurity located in coaxial quantum well wire. A uniform magnetic field is applied along the axis of the wire. The different effective masses in the different regions of the CQWW are taken into consideration. The Schrödinger radial equation in the absence of the impurity has been solved analytically in the different regions instead of using the numerical methods employed in earlier treatments. In the presence of the impurity, the trial wavefunction has been taken in a new form in addition to the conventional form used in previous work. The new form has the advantage of satisfying the boundary conditions at all the interfaces in the case of different masses. It tends to raise the results of binding energy so that they approach the exact solution from below. Moreover, some new analytical expressions for the energy expectation value and for the binding energy have been derived