Modified quantum mechanics of small composite systems

Boundary conditions on radial wave functions are considered for a particle bound by a central potential. It is argued that the usual condition at the origin needs modification for systems of small intrinsic size. This affects s-states, especially the ground state. With the obtained modification the virial theorem is imposed rather than derived. As an illustration the central rectangular well potential is treated and applied to the nucleon. Its soft electromagnetic structure can be largely explained while quark confinement holds despite moderate strength of the potential. A discussion follows. (Auth.)