Relativistic and nonrelativistic one-dimensional systems of particles of the same mass interacting through instantaneous contact interactions are considered. For the relativistic interaction, we assume a combination of a Lorentz scalar and a vector. The mass and interaction strength are chosen such that the deuteron is simulated; the relativistic and nonrelativistic "deuteron" models have the same binding energy and practically the same structure. The relativistic and nonrelativistic Hartree–Fock equations can both be solved analytically. For certain combinations of the Lorentz scalar and vector interactions, the difference between the relativistic and nonrelativistic results can be appreciable.