# Aspects of Quantum System Theory

## Abstract

Multi-component systems of the microscopic world, i. e. high-dimensional quantum systems, can be described by various formalisms, which are in the end equivalent. A formalism on the basis of a differential evolution equation, the *Schrödinger* equation, as well as a formalism on the basis of a path integral, the *Feynman* path integral, is possible, where this integral formalism represents nothing else but the method of Green’s function. By some kinds of transformation one can get other possible formalisms like the *Heisenberg* formalism or the interaction formalism. In this chapter in particular I want to look at the method of *R. P. Feynman*, and I want to present the extension of the introduced method of integral calculation (see chapter 4) to quantum systems. In this context a statistical basic function will be introduced, which contains all statistically relevant information of both quantum systems and non-microscopic systems (like laser systems or thermodynamic systems). Thus, the universality of the introduced concept of system theory will become evident, and therefore a pathway to quantum systems is given. Furthermore, I will again attach importance to the problem of interrelation between equations of the *Schrödinger* and the *Fokker-Planck* type.

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