''Asymptotic freedom'' in quantum mechanics

Sum rules in quantum mechanics true for nonsingular potentials are considered. The physical content of sum rules is reduced to the fact that at small distances the interaction energy is small as compared with kinetic energy and the interaction may be considered as perturbation. In this sense there exists a direct analogy with quantum chromodynamics sum rules, previously discussed in detail. The common character of the situation found for the first time in the case of quantum chromodynamics: if the interaction grows fast with the distance increase one may obtain sum rules which on the one hand use Born approximation of interaction, on the other - they are saturated by one-two low levels