Theoretical Physics 6: Quantum Mechanics - Basics

Kurt Gottfried, Tung‐Mow Yan

Lee Chang, Mo‐Lin Ge

"Owing to efforts in both theoretical and experimental research, a better understanding of the interpretation and many fundamental principles of quantum mechanics has been achieved. These include the complementarity principle, the geometrical phase, the topological phase, the boundary between quantum and classical mechanics, quantum mechanics on the macroscopic level, and so on. Part of this book is devoted to introducing these developments. Significant progress in the frontier research in various branches of physics has been achieved by making use of the insights and judgements originating from quantum mechanics. Part of this book is devoted to introducing some of these fields, namely quantum information, cavity quantum electrodynamics, the quantum Hall effect and the Bose-Einstein condensation. Basic physical ideas and methods are emphasized, instead of going into technical details. The Yang-Baxter system has become a prosperous field of mathematical physics. The last part of the book is devoted to introducing its application to some basic problems in quantum mechanics, and again basic physical ideas are emphasized."

Andrew Whitaker

Andrei Yu. Khrennikov

In the nineteenth century (in the process of transition from mechanics to the field theory), the German school of theoretical physics confronted problems similar to the basic problems in the foundations of quantum mechanics (QM). Hertz tried to resolve such problem through analysis of the notion of a scientific theory and interrelation of theory and experiment. This analysis led him to the Bild (image) conception of theory (which was later essentially developed, but also modified by Boltzmann). In this paper, we claim that to resolve the basic foundational problems of QM, one has to use the Bild conception and reject the observational viewpoint on physical theory. As an example of a Bild theory underlying QM (treated as an observational theory), we consider prequantum classical statistical field theory (PCSFT): theory of random subquantum fields.

Zhaoxu Ji, Huanguo Zhang

Since its establishment, quantum mechanics has developed for a century and has a very large theoretical system,but the phenomenon of quantum mechanics still lacks a generally accepted explanation,which undoubtedly shows that the existing theoretical system is incomplete.Inspired by ancient Chinese philosophy, we propose a new theoretical framework based onsome existing principles of classical physics and quantum mechanics,which opens a new perspective for the interpretation of quantum mechanics.Furthermore, based on this framework, we design a new algorithm for entanglement swapping,the basic idea of which is to derive two entangled states created by entanglement swapping from all possible observations.We demonstrate the basic idea of the algorithm through the entanglement swapping between two bipartite entangled states,and derive the results of the entanglement swapping between two Bell states,which is surprisingly consistent with those obtained through algebraic calculations.Of course, through the proposed algorithm, the correctness of the proposed theoretical framework can be verified.Our work will contribute to a deeper exploration of the mysteries of nature, including quantum mechanical phenomena.