Textbook. -Rostov-on-Don, 2008. 388 s. Fully Recognized . Annotation. Scientific literature, On the fundamental problems of quantum physics , new quantum effects and their applications , widely uses mathematical apparatus and theoretical methods, not studied at the proper level in standard courses of quantum theory and insufficiently described in standard textbooks This book is designed to fill an existing gap. It focuses on the non-examining of specific quantum phenomena, what is easy to find in any textbook on quantum mechanics, A detailed description of the physical foundations of quantum mechanics , its mathematical apparatus, necessary for the study of modern literature , methods of using this apparatus to describe the main non-relativistic microobjects and axiomatics , establishing a relationship between the mathematical apparatus and the characteristics of microobjects. The textbook is designed for graduate students, undergraduate and undergraduate students who want to conduct scientific work in the following areas of modern physics: fundamental problems of quantum physics, physics of nanostructures and quantum computers.