Terms of the one-dimensional molecular $D_2^-$-ion in a longitudinal magnetic field

In the framework of a model of zero-range potential, the problem of electron bound states in the field of two $D^0$-centers (a two-center problem) in a semiconductor quantum wire with a parabolic confinement potential in the presence of a longitudinal magnetic field is considered. Equations describing the $g$- and $u$-terms that correspond to symmetric and antisymmetric states of an electron localized at the $D_2^-$-center are obtained. The terms as functions of the magnetic field strength in the quantum wire with the parabolic confinement potential are studied.