Classical & Quantum Mechanics

R. Asokamani

Qian Shang-Wu

By comparison between equations of motion of geometrical optics(GO)and that of classical statistical mechanics(CSM),we find that there should be an analogy between GO and CSM instead of GO and classical mechanics (CM).Furthermore,by comparison between the classical limit(CL)of quantum mechanics(QM)and CSM,we find that CL of QM is CSM not CM,hence we demonstrate that QM is a natural generalization of CSM instead of CM.

N. Rosen

James T. Cushing

The ubiquity of chaos in classical mechanics (CM), as opposed to the situation in standard quantum mechanics (QM), might be taken as speaking against QM being the fundamental theory of physical phenomena. Bohmian mechanics (BM), as a formulation of quantum theory, may clarify both the existence of chaos in the quantum domain and the nature of the classical limit. Two interesting possibilities are (i) that CM and classical chaos are included in and underwritten by quantum mechanics (BM) or (ii) that BM and CM simply possess a common region of (noninclusive) overlap. In the latter case, neither CM nor QM alone would be sufficient, even in principle, to account for all of the physical phenomena we encounter. In this talk I shall summarize and discuss the implications of some recent work on chaos and on the classical limit within the framework of BM.

Marmo, G, David Martı́n de Diego, Lecanda, Miguel

Peter Renkel

The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it is desirable to build a bridge from CM to QM. This paper presents a generalization of CM to QM. It starts from the generalization of a point-like object and naturally arrives at the quantum state vector of quantum systems in the complex valued Hilbert space, its time evolution and quantum representation of a measurement apparatus of any size. Each time, when generalization is performed, there is a possibility to develop new theory giving up most simple generalizations. It is shown that a measurement apparatus is a special case of a general quantum object. An example of a measurement apparatus of an intermediate size is considered in the end.