THE REGULATED 4-PARAMETER ONE-DIMENSIONAL POINT INTERACTION

The general four-parameter point interaction in one-dimensional quantu m mechanics is regulated. It allows the exact solution, but not the pe rturbative one. We conjecture that this is due to the interaction not being asymptotically free. We then propose a different breakup of unpe rturbed theory and interaction, which now is asymptotically free but l eads to the same physics. The corresponding regulated potential can be solved both exactly and perturbatively, in agreement with the conject ure.