Lepton-spectrum-inducing potentials and the family problem

Examples of potentials are given which give rise to at least three consecutive s-states as lowest bound states. They have not to be singular or long ranged in any sense. The incorporation of a level spacing in accordance with the phenomenological mass spectrum of the charged leptons appears more difficult. Trying to solve this problem by using the inverse scattering transformation leads to features which seem to indicate the necessity of a relativistic treatment. The small lepton radius, on the other hand, does not pose any problem. It is possible that also p-states appear which should have a distinct experimental signature.