UNCERTAINTY RELATIONS FOR WAVE-FUNCTIONS

It is proved that when the Hilbert space of quantum mechanics is a reproducing kernel Hilbert space of functions defined on the phase space, the generating function of the entropy can be used as a measure of the concentration of the wavefunctions in the phase space. The sharp upper bound obtained for the generating function of the entropy proves that the wavefunctions cannot be arbitrarily peaked in the phase space. The most peaked wavefunctions are those defined by the reproducing kernels.