The arising of a Rashba-like coupling, a Zeeman-like term and a Darwin-like term induced by Lorentz symmetry breaking effects in the non-relativistic quantum dynamics of a spin-1/2 neutral particle interacting with external fields is studied. Moreover, the influence of a Rashba-like coupling induced by a Lorentz symmetry violation background on the Tan–Inkson potential [W.-C. Tan and J. C. Inkson, Semicond. Sci. Technol. 11, 1635 (1996)] is discussed.