Matter Structuring in Nano Scales and Fundamental Constants of Physics

It is generally believed that all fundamental constants are the same everywhere. The experience with the variable velocity of light suggests however that such a belief may not be justified. In spite of that the possibility that the Planck constant may be different at different scales and at different places of our universe never was discussed. Since the constancy in space of the Planck constant cannot be checked in direct experiments the only way of proving its constancy or variability is to consider theories which allow to vary this fundamental constant. The comparison of the derived results with the corresponding results of standard quantum mechanics solves then the problem. In the talk we present an approach to quantum mechanics which allows to vary the Planck constant. Due to troubles with exact solutions our results have approximate character only. The possible consequences for practical nanotechnology, for theories of many-electron atoms and for large scale structures of the universe are discussed.