[en] The states of the electron localized at a donor in the quantum constriction with parabolic electron potential in the presence of a magnetic field that is longitudinal with respect to the axis of the constriction are considered. The dispersion relation for electrons was derived analytically in the context of the model of the zero-radius potential taking into account the effect of a magnetic field on the D^(-) state in the quantum constriction. It is found that the singularity in the electron spectrum in the quantum constriction manifests itself in the dependences of the binding energy of the D^(-) state and the edge of the extrinsic-absorption band on the effective length of the constriction. The evolution of both the binding energy of the D^(-) state and the spectrum of intrinsic magnetooptical absorption in the quantum constriction as the strength of a longitudinal magnetic is varied is studied. The results are compared with those in the case of the D^(-) state in a quantum wire