The infinite well and Dirac delta function potentials as pedagogical,mathematical and physical models in quantum mechanics

The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems.     

The mathematical basis of physical laws: Relativistic mechanics,quantum mechanics,the Lorentz force,Maxwell's equations and non-electromagnetic forces for spin zero particles

We show that defining the observed proper velocity and acceleration of a spin zero particle as the first and second derivatives of the classical expectation value for the space-time position vector, defined on a manifold carrying the Lorentz metric, with respect to a conditioning parameter , yields directly: a Lorentz and gauge invariant quantum mechanics, the Lorentz force, Maxwell's equations and a field equation for a non-electromagnetic potential. This also provides a new basis for gauge conditions in the field theory and shows that only the Lorentz gauge condition is admissible in electromagnetic theory.     

Precision atomic mass spectrometry with applications to fundamental constants, neutrino physics, and physical chemistry

We present a summary of precision atomic mass measurements of stable isotopes carried out at Florida State University. These include the alkalis ⁶Li, ²³Na, ^39,41K, ^85,87Rb, ¹³³Cs; the rare gas isotopes ^84,86Kr and ^{129,130,132,136}Xe; ^17,18O, ¹⁹F, ²⁸Si, ³¹P, ³²S; and various isotope pairs of importance to neutrino physics, namely ^74,76Se/^74,76Ge, ¹³⁰Xe/¹³⁰Te, and ¹¹⁵In/¹¹⁵Sn. We also summarize our Penning trap measurements of the dipole moments of PH^?+? and HCO^?+?.     

The multifractal analysis of Gibbs measures: Motivation,mathematical foundation,and examples

We first motivate the study of multifractals. We then present a rigorous mathematical foundation for the multifractal analysis of Gibbs measures invariant under dynamical systems. Finally we effect a complete multifractal analysis for several classes of hyperbolic dynamical systems. (c) 1997 American Institute of Physics.     

Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology

We investigate the effect of varying boundary conditions on the renormalization group flow in a recently developed noncommutative geometry model of particle physics and cosmology. We first show that there is a sensitive dependence on the initial conditions at unification, so that, varying a parameter even slightly can be shown to have drastic effects on the running of the model parameters. We compare the running in the case of the default and the maximal mixing conditions at unification. We then exhibit explicitly a particular choice of initial conditions at the unification scale, in the form of modified maximal mixing conditions, which have the property that they satisfy all the geometric constraints imposed by the noncommutative geometry of the model at unification, and at the same time, after running them down to lower energies with the renormalization group flow, they still agree in order of magnitude with the predictions at the electroweak scale.     

Some recent developments in the applications of Mössbauer spectroscopy to physical metallurgy

We discuss the applications of M?ssbauer spectroscopy to physical metallurgy using three examples: fcc γ-Fe; hydrogen in metals; amorphous metals.     

Expansion of the distance between two points in spheroidal functions as applied to problems of mathematical physics

A complete set of biharmonic functions is constructed in spheroidal coordinates. The distance between two points and its inverse value are expanded into a double series in terms of such functions. Possible applications in the theory of elasticity, in astrophysics, and other fields of mathematical physics are pointed out.     

粒子物理和宇宙学中的两片乌云——谈暗物质和暗能量

宇宙暗物质和暗能量是21世纪粒子物理和宇宙学研究中的两个重大的科学问题.文章首先简述了宇宙学研究的历史和现状以及对粒子物理学提出的新的挑战,接着较详细地介绍了暗物质、暗能量和反物质相关的科学问题以及在国际上这个研究领域近年来所取得的进展,最后展望了中国在暗物质和暗能量实验探测研究方面的前景.     

The Bragg medal and prize of the Institute of physics and the physical society, 1971

The following citation is quoted from The Bulletin of the Institute of Physics and The Physical Society, Vol. 22, p. 94, February 1971, with deep appreciation of the honour.     

Laser shock processing: a review of the physics and applications

Developed since the beginning of the 1970s in the United States (Battelle, Columbus), laser shock processing (LSP) is being extensively studied in France in order to improve the mechanical properties of metallic surfaces of dense or porous materials. This paper reviews the considerable data on LSP which has been obtained in recent years and provides an exhaustive account of current trends concerning the physics, the mechanics and the applications involved. After presenting some general and specific data regarding the physical principles of laser shock (laser system, plasma physics, pressure generation, physical limits) and mechanical effects induced (experimental and theoretical) on different materials, the efficiency of the process is illustrated through two potential industrial applications linked with modifications of surface states: fatigue and wear resistance of metals. Experience with LSP applications shows that, because it uses safe surface geometries and provides greater affected depths, LSP is about to emerge as a real alternative to classical treatments.     

The physics of DNA: Onset of soliton-like excitations,chain relative disorder,and basis for a statistical mechanics of the macromolecule

A dual approach for studying the dynamics and function of DNA is proposed. Soliton-like excitations may occur under certain conditions and, via an electromagnetic signal that can modulate the soliton energy, the transition B-DNA (resting state) A-DNA (active state) can take place. On the other hand, the Hamiltonian describing this transition can be used to construct an entropy operator for DNA and thus assess its state of relative disorder and its relationship to DNA function. Biological and medical applications of this study are put forward, as well as predictions for experimentally testing the model.     

The physical and mathematical foundations of the intranuclear cascade model algorithm

The physical and mathematical approximations underlying the intranuclear cascade model (INC) algorithm are considered here. The INC algorithm is shown to be a version of Monte-Carlo calculations for multiple integrals which provide the solutions of the system of coupled equations for many-body distribution functions. The conditions under which these equations are derived from the Schrödinger many-body equations are analysed, with special emphasis on the finite size of the nuclear system.     

第1届亚洲物理奥林匹克竞赛力学实验题解答及分析

介绍第1届亚洲物理奥林匹克竞赛力学实验题及其解答,并分析了该实验题的设计思想、特点与要求.