31 research outputs found
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