波粒二象性的复兴：结果、应用和相对论性量子力学
Wave-Particle Duality Revitalized: Consequences, Applications and Relativistic Quantum Mechanics
摘要：
提出的文件介绍了德布罗意的概念的波粒二象性和物质波在1923年未观察到的不足之处。一般公认的量子能量或频率表达式hν=γ mc 2被证明不适用于物质波，而只适用于光子。详细研究了物质波的超光速相速度表达式c ~ 2/ \u{psion}，并指出其不足。对德布罗意理论的不足之处进行了修正，并对光波与物质波的类比实现进行了改进，给出了修正后的物质波的频率和相速度表达式。文中还给出了修正频率和相速度表达式的数学证明。根据所提出的概念，一个波粒二象性的图片，阐明了问题耦合的波粒二象性，存在于文献中。因此，粒子类型的性质被证明是波的唯一特征，独立于物质的存在。在物质波的频率表达式中引入的修改导致自由运动粒子及其能量算子的波函数表达式的变化，并有适当的理由。本文提出了运动物体动能和动量之间的一种新关系，并将其应用于引入新的广义和相对论量子机械波方程。这些方程在束缚态量子力学系统中的应用，提供了关于这类系统中粒子的一般和相对论行为的信息。此外，所提出的波动方程也可以转化为薛定谔方程和狄拉克方程。薛定谔方程、狄拉克方程和所提出的方程与普适波动方程的相互关系也被提出。
英文摘要：
The proposed paper presents the unobserved inadequacies in de Broglie's concepts of wave-particle duality and matter waves in the year 1923. The commonly admitted quantum energy or frequency expression hν=γmc2 is shown to be inappropriate for matter waves and is acceptable only for photons. The superluminal phase velocity expression c2/\u{psion}, for matter waves, is investigated in detail and is also reported to be inadequate. The rectifications in the inadequate concepts of de Broglie's theory and refinements in the analogy implementation between light waves and matter waves are presented, which provides the modified frequency and phase velocity expression for matter waves. Mathematical proofs for the proposed modified frequency and phase velocity expression are also presented. In accordance with the proposed concepts, a wave-particle duality picture is presented which elucidates the questions coupled with the wave-particle duality, existing in the literature. Consequently, particle type nature is shown to be a characteristic of waves only, independent from the presence of matter. The modifications introduced in the frequency expression for matter waves leads to variation in the wave function expression for a freely moving particle and its energy operators, with appropriate justifications. A new relation between the Kinetic energy and Momentum of the moving body is proposed and is subsequently applied to introduce novel General and Relativistic Quantum Mechanical Wave Equations. Applications of these equations in bound state quantum mechanical systems provide the information regarding particle's general and relativistic behavior in such systems. Moreover, the proposed wave equations can also be transformed into Schrödinger's and Dirac's equations. The interrelation of Schrödinger's, Dirac's and proposed equations with the universal wave equation is also presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
