Abundant Computational and Numerical Solutions of the Fractional Quantum Version of the Relativistic Energy-Momentum Relation

2021 ◽  
pp. 39-86
Author(s):  
Mostafa M.A. Khater ◽  
Raghda A.M. Attia ◽  
Saud Owyed ◽  
Abdel-Haleem Abdel-Aty
Keyword(s):  
Numerical Solutions ◽  
Relativistic Energy ◽  
Fractional Quantum ◽  
Quantum Version ◽  
Momentum Relation

scholarly journals Better Quantum Mechanics ? Thoughts on a New Definition of Momentum That Makes Physics Simpler and More Consistent

2019 ◽  
Author(s):  
Espen Haug
Keyword(s):  
Rest Mass ◽  
Total Momentum ◽  
Relativistic Wave Equation ◽  
Relativistic Energy ◽  
Relativistic Wave ◽  
Compton Wavelength ◽  
Definition Of ◽  
De Broglie Wavelength ◽  
Logical Perspective ◽  
Momentum Relation

We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.

scholarly journals Better Quantum Mechanics ? Thoughts on a New Definition of Momentum That Makes Physics Simpler and More Consistent

2019 ◽  
Author(s):  
Espen Haug
Keyword(s):  
Rest Mass ◽  
Total Momentum ◽  
Relativistic Wave Equation ◽  
Relativistic Energy ◽  
Relativistic Wave ◽  
Compton Wavelength ◽  
Definition Of ◽  
De Broglie Wavelength ◽  
Logical Perspective ◽  
Momentum Relation

We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.

scholarly journals On the Complementary Wave Interpretation of the Dirac Equation

2013 ◽  
Vol 14 ◽  
pp. 103-115
Author(s):  
D.L. Bulathsinghala ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Special Theory ◽  
Uncertainty Relations ◽  
Relativistic Energy ◽  
Theory Of Relativity ◽  
Position Uncertainty ◽  
Time Arrow ◽  
New Hypothesis ◽  
Momentum Relation

The Dirac equation consistent with the principles of quantum mechanics and the special theory of relativity, introduces a set of matrices combined with the wave function of a particle in motion to give rise to the relativistic energy-momentum relation. In this paper a new hypothesis, the wave function of a particle in motion is associated with a pair of complementary waves is proposed. This hypothesis gives rise to the same relativistic energy-momentum relation and achieves results identical to those of Dirac. Additionally, both the energy-time and momentum-position uncertainty relations are derived from the complementary wave interpretation. How the complementary wave interpretation of the Dirac equation is related to the time-arrow and the four-vectors are also presented.

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

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