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Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

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Journal of Modern Physics 2024年第6期15卷 765-795页

作者： André Michaud Service de Recherche Pé dagogique Qu&#233bec Canada

Analysis of the initial stages of the logical process followed by Louis de Broglie in establishing the electron phase wave equation in his 1924 thesis, which triggered the development of wave mechanics when Erwin Schrödinger formalized this concept with his vectorial wave equation. This development was soon followed by Quantum mechanics, when Schrödinger proved that the Matrix mechanics independently developed by Werner Heisenberg was equivalent to wave mechanics, with both theories leaving room for some degree of uncertainty as to the physical localization of the moving electron. This is what led Heisenberg to also formalize the Uncertainty Principle to take this situation into account. This principle was soon regarded as a fundamental axiomatic principle that seemed to make further exploration of the subatomic level of magnitude appear impossible to most researchers. We will analyze in this article the reason why the phase-wave velocity established by de Broglie generated this uncertainty in the localization of the moving electron in light of the current state of knowledge on the behavior of the electron in motion, in view of establishing the relevance of maintaining the Uncertainty Principle in the study of the subatomic level of magnitude.

关键词： Phase wave Velocity wave mechanics Matrix mechanics Quantum mechanics Uncertainty Principle

Generalized Quantization Condition

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Chinese Physics Letters 2005年第10期22卷 2465-2468页

作者：梁铮曹庄琪邓晓旭沈启舜 Institute of Optics and Photonics Shanghai Jiao Tong University Shanghai 200240

On the basis of analytical transfer matrix theory, we fine a generalized quantization condition. By introducing a new type of modified momentum, our quantization condition has the same form as the Bohr Sommerfeld form... 详细信息

关键词： wave mechanics

Initial-Value Problem of a Coupled Dispersionless System： Dynamical System Approach

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Chinese Physics Letters 2009年第3期26卷 54-57页

作者： Kuetche Kamgang Victor Ecole Nationale Supérieure Polytechnique University of Yaounde I PO Box 8390 Cameroon Department of Physics Faculty of Science University of Yaounde I PO Box 812 Cameroon The Abdus Salam International Centre for Theoretical Physics PO Box 586 Strada Costiera II-34014 Trieste Italy

We investigate the dynamical behaviour of a coupled dispersionless system （CDS） by solving its initial-value problem following a dynamical system approach. As a result, we unearth a typical miscellaneous travelling waves including the localized and periodic ones. We also investigate the energy density of such waves and find that under some boundary conditions, the localized waves moving towards positive direction are more stable than the periodic waves which on contrary stand for the most conditions. stable travelling waves in another situation of boundary conditions.

关键词： PARTIAL differential equations INITIAL value problems -- Numerical solutions DYNAMICS LOCALIZED waves wave mechanics BOUNDARY value problems

Stochastic Signal Induced Multiple Spatial Coherence Resonances and Spiral waves in Excitable Media

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Chinese Physics Letters 2009年第3期26卷 46-49页

作者：李玉叶张慧敏魏春玲杨明浩古华光任维 Department of Mathematics Institute of Chifeng Chifeng 024000 College of Life Science Shaanxi Normal University Xi'an 710062

Multiple spatial coherence resonances and spiral waves with various temporal-spatial structures are simulated in a two-dimensional network of excitable cells driven by a stochastic signal. The relationship between the multiple resonances and correspondingly different transitions of the spiral wave are elucidated. The results further provide a possible approach of applications of stochastic signal to evoke pattern transitions in excitable media.

关键词： SIGNAL processing EXCITED state chemistry COHERENCE (Optics) OPTICAL resonance wave mechanics STOCHASTIC processes

Nonlinear Shock and Kink waves with Complete Coriolis Force in Earth＇s Atmosphere

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Chinese Physics Letters 2009年第3期26卷 310-312页

作者：于鑫赵强 School of Physics Peking University Belting 100871

Nonlinear waves in a Boussinesq fluid model which includes both the vertical and horizontal components of Coriolis force are studied by using the semi-geostrophic approximation and the method of travelling-wave solution. Taylor series expansion has been employed to isolate the characteristics of the linear Rossby waves and to identify the nonlinear shock and kink waves. The KdV-Burgers and the compound KdV-Burgers equations are derived, their shock wave and kink wave solution are also obtained.

关键词： SHOCK waves NONLINEAR waves CORIOLIS force ATMOSPHERE wave mechanics APPROXIMATION theory EARTH (Planet)

Dynamics of Incoherent Photovoltaic Spatial Solitons

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Chinese Physics Letters 2009年第3期26卷 132-135页

作者：张贻齐卢克清张美志李可昊刘爽张彦鹏 State Key Laboratory of Transient Optics and Photonics Xi'an Institute of Optics and Precision Mechanics Chinese Academy of Sciences Xi'an 710119 Optoelectronic Technology Department Optoelectronic Tracking Technology Research Center Xi'an Institute of Optics and Precision Mechanics Chinese Academy of Sciences Xi'an 710119 Graduate University of Chinese Academic of Sciences Beijing 100049 Department of Electronic Science and Technology Xi'an Jiaotong University Xi'an 710049

Propagation properties of bright and dark incoherent beams are numerically studied in photovoltaic-photorefractive crystal by using coherent density approach for the first time. Numerical simulations not only exhibit that bright incoherent photovoltaic quasi-soliton, grey-like incoherent photovoltaic soliton, incoherent soliton doublet and triplet can be established under proper conditions, but also display that the spatial coherence properties of these incoherent beams can be significantly affected during propagation by the photovoltaic field.

关键词： SOLITONS wave mechanics PHOTOVOLTAIC power generation PHOTOREFRACTIVE materials CRYSTAL optics COHERENCE (Optics) NUMERICAL analysis

The Dynamics of wave-Particle Duality

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Journal of Applied Mathematics and Physics 2018年第9期6卷 1840-1859页

作者： Adriano Orefice Raffaele Giovanelli Domenico Ditto Department of Agricultural and Environmental Sciences (DISAA) University of Milan Milano Italy

Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and interference process. In the case of wave mechanics, de Broglie’s merging of Maupertuis’s and Fermat’s principles (see Section 3) provides, without resorting to the probability-based guidance-laws and flow-lines of the Bohmian theory, the simple law addressing particles along the Helmholtz rays of the relevant matter waves. The purpose of the present research was to derive the exact Hamiltonian ray-trajectory systems concerning, respectively, classical electromagnetic waves, non-relativistic matter waves and relativistic matter waves. We faced then, as a typical example, the numerical solution of non-relativistic wave-mechanical equation systems in a number of numerical applications, showing that each particle turns out to “dances a wave-mechanical dance” around its classical trajectory, to which it reduces when the ray-coupling is neglected. Our approach reaches the double goal of a clear insight into the mechanism of wave-particle duality and of a reasonably simple computability. We finally compared our exact dynamical approach, running as close as possible to Classical mechanics, with the hydrodynamic Bohmian theory, based on fluid-like “guidance laws”.

关键词： Helmholtz Equation wave Potential Hamilton-Jacobi Equation wave mechanics De Broglie’s Duality Matter waves Guidance Laws Schrodinger Equations Klein-Gordon Equation