4-PARAMETER POINT-INTERACTION IN 1D QUANTUM-SYSTEMS

We construct a four-parameter point-interaction for a non-relativistic particle moving on a fine as the limit of a short-range interaction with a range tending toward zero. For particular choices of the parameters, we can obtain a delta-interaction or the so-called delta'-interaction. The Hamiltonian correSponding to the four-parameter point-interaction is shown to correspond to the four-parameter self-adjoint Hamiltonian of the free particle moving on the line with the origin excluded.