  Within the framework of staircase infinitely deep (SIW) potential well model
the effect of dielectric constant mismatch between the size-quantized
semiconducting wire, coating and surrounding environment on impurity binding
energy is considered. Calculations are done in both the absence and presence of
magnetic field applied along the wire axis. By the variation method the
dependences of binding energy of hydrogen-like impurity located on the wire
axis on the alloy concentration, effective mass ratio, dielectric constant
mismatch and magnetic field are found for the GaAs-Ga_{1-x}Al_{x}AS system.
