Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

普通物理力学和理论力学的整合

理顺物理类普通物理力学和理论力学的关系,将理论力学中的牛顿力学部分基本上都归入普物力学,加强分析力学部分,并增加非线性力学,改名为分析力学．     

Toward a micro realistic version of quantum mechanics. Part I

This paper investigates the possibility of developing a fully micro realistic version of elementary quantum mechanics. I argue that it is highly desirable to develop such a version of quantum mechanics, and that the failure of all current versions and interpretations of quantum mechanics to constitute micro realistic theories is at the root of many of the interpretative problems associated with quantum mechanics, in particular the problem of measurement. I put forward a propensity micro realistic version of quantum mechanics, and suggest how it might be possible to discriminate, on experimental grounds, between this theory and other versions of quantum mechanics.     

Nambu Mechanics in the Lagrangian Formalism

A Lagrangian formulation is presented as the counterpart of the Hamiltonian onefor Nambu mechanics which is a natural generalization of Hamiltonian mechanics.If we postulate the existence of plural Lagrangians corresponding to the existenceof plural Hamiltonians, we can formulate the Lagrangian formalism in Nambumechanics as well as in Hamiltonian mechanics. Here, in terms of exteriordifferentiation, Nambu mechanics can be formulated in a completely parallel wayto ordinary analytical mechanics, including generalized Legendre transformations.     

量子力学混合态表象

在以往的文献中量子力学的表象都是纯态表象,在本文中我们从算符的合理排序和概率统计的正态分布思想出发,首次提出了量子力学混合态表象的概念,并证明了其完备性和正交性.量子力学混合态表象的优点是可以反映算符的多种表示以及其相应的排序规则.     

A Continuous Transition Between Quantum and Classical Mechanics. I

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of mechanics which provides a continuous transition between quantum and classical mechanics via environment-induced decoherence.     

The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part III. Idealizations. Hilbert space representation

We illustrate the application of the conceptual analysis (CA) method outlined in Part I by the example of quantum mechanics. In the present part the Hilbert space structure of conventional quantum mechanics is deduced as a consequence of postulates specifying further idealized concepts. A critical discussion of the idealizations of quantum mechanics is proposed. Quantum mechanics is characterized as a “statistically complete” theory and a simple and elegant formal recipe for the construction of the fundamental mathematical apparatus of quantum mechanics is formulated. Our analysis may also lead to a criticism of quantum mechanics as a “strongly idealized” theory. A critical analysis of the fundamental structure of quantum mechanics seems an indispensable and natural starting point for the construction of new theories. A major technical problem in a more general application of the CA method is the lack of mathematical representation theorems for more general algebraic structures.     

Consistent histories and operational quantum theory

In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and give some general comments about it. We investigate to what extent the consistent histories scheme is compatible with the results of the operational formulation of quantum mechanics. According to the operational approach, nonrelativistic quantum mechanics is most generally formulated in terms of effects, states, and operations. We formulate a generalized consistent histories theory using the concepts and the terminology which have proven useful in the operational formulation of quantum mechanics. The logical rule of the logical interpretation of quantum mechanics is generalized to the present context. The algebraic structure of the generalized theory is studied in detail.     

A Stochastic Mechanics Based on Bohm‧s Theory and its Connection with Quantum Mechanics

We construct a stochastic mechanics by replacing Bohm‧s first-order ordinary differential equation of motion with a stochastic differential equation where the stochastic process is defined by the set of Bohmian momentum time histories from an ensemble of particles. We show that, if the stochastic process is a purely random process with n-th order joint probability density in the form of products of delta functions, then the stochastic mechanics is equivalent to quantum mechanics in the sense that the former yields the same position probability density as the latter. However, for a particular non-purely random process, we show that the stochastic mechanics is not equivalent to quantum mechanics. Whether the equivalence between the stochastic mechanics and quantum mechanics holds for all purely random processes but breaks down for all non-purely random processes remains an open question.     

一维无限深方势阱中粒子动量概率分布引出的问题

本文强调泡利关于一维无限深方势阱中粒子动量的结论与标准量子力学的逻辑推论不一致,而标准量子力学是自洽的。指出,当我们在一个量子态上掺入某种直观的经典力学内容时要很谨慎。至于对量子力学本身,至今尚无一种公认的诠释。     

What Is Bohmian Mechanics

Bohmian mechanics is a quantum theory with a clear ontology. To make clear what we mean by this, we shall proceed by recalling first what are the problems of quantum mechanics. We shall then briefly sketch the basics of Bohmian mechanics and indicate how Bohmian mechanics solves these problems and clarifies the status and the role of the quantum formalism.     

Quaternionic quantum mechanics is consistent with complex quantum mechanics

Quaternionic quantum mechanics is investigated in the light of the great success of complex quantum mechanics. It is shown that to reproduce the results of complex quantum mechanics, quaternionic quantum mechanics must contain complex quantum mechanics.     

力学综合课程建设的研究和实践

简述了我校物理系进行力学综合课程建设的基本思想和措施，以及建立将普通物理力学、理论力学和量子力学基础综合成一门课程的新的教学内容结构体系的具体做法．这样做，不但大大减少了重复内容和课时。而且有助于学生从整体上把握力学理论的基本框架，有助于培养学生的综合研究能力和创新能力。     

The Frame of Fixed Stars in Relational Mechanics

Relational mechanics is a gauge theory of classical mechanics whose laws do not govern the motion of individual particles but the evolution of the distances between particles. Its formulation gives a satisfactory answer to Leibniz’s and Mach’s criticisms of Newton’s mechanics: relational mechanics does not rely on the idea of an absolute space. When describing the behavior of small subsystems with respect to the so called “fixed stars”, relational mechanics basically agrees with Newtonian mechanics. However, those subsystems having huge angular momentum will deviate from the Newtonian behavior if they are described in the frame of fixed stars. Such subsystems naturally belong to the field of astronomy; they can be used to test the relational theory.     

Photon wavelength, information transport speed, and mass. An information mechanics perspective

In Newton's mechanics, Maxwell's electromagnetism, Einstein's relativistic mechanics, quantum mechanics, and Kantor's information mechanics (IM), the speed of light in vacuumc has been treated as independent of wavelength. However, in IM, the transport of information by means of an electromagnetic signal appears to offer a perspective for reconsidering photon information transport speed, extending the concept of (rest) mass to treat the photon as having a mass of 1 bit.     

On the Classical Limit of Quantum Mechanics

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper, we shall formulate the classical limit as a scaling limit in terms of an adimensional parameter ε. We shall take the first steps toward a comprehensive understanding of the classical limit, analyzing special cases of classical behavior in the framework of a precise formulation of quantum mechanics called Bohmian mechanics which contains in its own structure the possibility of describing real objects in an observer-independent way.