Aspects of Quantum System Theory
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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