Electronic structure of two-electron systems with the short-range repulsive interaction

We obtained exact analytic solutions of one-dimensional two-particle systems with Dirac-delta repulsive interaction in two typical potentials. It was shown that in these potentials there exists not any wave function symmetrical with respect to the particle exchange. There exist only anti-symmetrical solutions to these systems. Applied to electronic quantum dots, they imply that there exist spin triplet states only and spin singlet states are not allowed for this electronic repulsive interaction