Abstract
The existing analytical mathematical models and numerical modeling work are not able to resolve a significant number of problems, known as the classical problems of the nucleation theory. The described research has revealed the main cause of these problems, the classical models correctly show the initial stages of the development of nanoparticles, where the use of traditional continuum approach and potentials, parameterized on the basis of macroscopic properties of liquids usually is ungrounded. This research is based on a more accurate representation of the nature of the small nano objects which is that of quantum.