On the Equation H=mv^2 and the Fine Structure of the Hydrogen Atom

The recently introduced reconciliation of the theories of special relativity and wave mechanics implies that the mass-energy equivalence principle must be expressed mathematically as H = mv^2, where H is the total energy of a particle, m is its relativistic mass, and v is its velocity; not H = mc^2 as was widely believed. In this paper, the equation H = mv^2 will be used to calculate the energy levels in the spectrum of the hydrogen atom. It is demonstrated that the well-known Sommerfeld-Dirac formula is still obtained, but without the constant term m_0 c^2 that was originally present in the formula.Comment: V2: added a few comments in response to the questions that I receive

New Reflections on Electron's Energy and Wavefunction in the Hydrogen Atom

Schrodinger's equation predicts something very peculiar about the electron in the Hydrogen atom: its total energy must be equal to zero. Unfortunately, an analysis of a zero-energy wavefunction for the electron in the Hydrogen atom has not been attempted in the published literature. This paper provides such an analysis for the first time and uncovers a few interesting facts, including the fact that a "zero-energy wavefunction" is actually a quantized version of the classical wavefunction that has been known for decades

Specific Mathematical Aspects of Dynamics Generated by Coherence Functions

This study presents specific aspects of dynamics generated by the coherence function (acting in an integral manner). It is considered that an oscillating system starting to work from initial nonzero conditions is commanded by the coherence function between the output of the system and an alternating function of a certain frequency. For different initial conditions, the evolution of the system is analyzed. The equivalence between integrodifferential equations and integral equations implying the same number of state variables is investigated; it is shown that integro-differential equations of second order are far more restrictive regarding the initial conditions for the state variables. Then, the analysis is extended to equations of evolution where the coherence function is acting under the form of a multiple integral. It is shown that for the coherence function represented under the form of an nth integral, some specific aspects as multiscale behaviour suitable for modelling transitions in complex systems (e.g., quantum physics) could be noticed when n equals 4, 5, or 6

Relativistic Short Range Phenomena and Space-Time Aspects of Pulse Measurements

Particle physics is increasingly being linked to engineering applications via electron microscopy, nuclear instrumentation, and numerous other applications. It is well known that relativistic particle equations notoriously fail over very short space-time intervals. This paper introduces new versions of Dirac's equation and of the Klein-Gordon equation that are suitable for short-range phenomena. Another objective of the paper is to demonstrate that pulse measurement methods that are based on the wave nature of matter do not necessarily correlate with physical definitions that are based on the corpuscular nature of particles

Gaussian Curvature in Propagation Problems in Physics and Engineering

The computation of the Gaussian curvature of a surface is a requirement in many propagation problems in physics and engineering. A formula is developed for the calculation of the Gaussian curvature by knowledge of two close geodesics on the surface, or alternatively from the projection (i.e., image) of such geodesics. The formula will be very useful for problems in general relativity, civil engineering, and robotic navigation