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.

scholarly journals How Dirac's Seminal Contributions Pave the Way for Comprehending Nature's Deeper Designs

Quanta ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 88-100
Author(s):  
Mani L. Bhaumik
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Relativistic Equation ◽  
Special Theory ◽  
Particle Energy ◽  
Theory Of Relativity ◽  
Perfect Agreement ◽  
Wave Particle Duality

Credible reasons are presented to reveal that many of the lingering century old enigmas, surrounding the behavior of at least an individual quantum particle, can be comprehended in terms of an objectively real specific wave function. This wave function is gleaned from the single particle energy-momentum eigenstate offered by the theory of space filling universal quantum fields that is an inevitable outcome of Dirac's pioneering masterpiece. Examples of these well-known enigmas are wave particle duality, the de Broglie hypothesis, the uncertainty principle, wave function collapse, and predictions of measurement outcomes in terms of probability instead of certainty. Paul Dirac successfully incorporated special theory of relativity into quantum mechanics for the first time. This was accomplished through his ingenious use of matrices that allowed the equations of motion to maintain the necessary first order time derivative feature necessary for positive probability density. The ensuing Dirac equation for the electron led to the recognition of the mystifying quantized spin and magnetic moment as intrinsic properties in contrast to earlier ad hoc assumptions. The solution of his relativistic equation for the hydrogen atom produced results in perfect agreement with experimental data available at the time. The most far reaching prediction of the celebrated Dirac equation was the totally unexpected existence of anti-particles, culminating in the eventual development of the quantum field theory of the Standard Model that reveals the deepest secrets of the universe known to date. Quanta 2019; 8: 88–100.

scholarly journals Mössbauer experiments in a rotating system and physical interpretation of their results

2021 ◽  
pp. 34-43
Author(s):  
Alexander L. Kholmetskii ◽  
Tolga Yarman ◽  
Ozan Yarman ◽  
Metin Arik
Keyword(s):  
Energy Shift ◽  
Special Theory ◽  
Relativistic Energy ◽  
Theory Of Relativity ◽  
Rotating System ◽  
Rotating Systems ◽  
Extra Energy ◽  
Quantum Mechanical Description ◽  
Dilation Effect ◽  
The Moment

We discuss the results of modern Mössbauer experiments in a rotating system, which show the presence of an extra energy shift between the emitted and absorbed resonant radiation in addition to the relativistic energy shift of the resonant lines due to the time dilation effect in the co-rotating source and absorber with different radial coordinates. We analyse the available attempts to explain the origin of the extra energy shift, which include some extensions of special theory of relativity with hypothesis about the existence of limited acceleration in nature, with hypothesis about a so-called «time-dependent Doppler effect», as well as in the framework of the general theory of relativity under re-analysis of the metric effects in the rotating system, which is focused to the problem of correct synchronisation of clocks in a rotating system with a laboratory clock. We show that all such attempts remain unsuccessful until the moment, and we indicate possible ways of solving this problem, which should combine metric effects in rotating systems with quantum mechanical description of resonant nuclei confined in crystal cells.

scholarly journals Schrodinger Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Inertial Frame ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Klein Gordon

Schrodinger equation is a wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Schrodinger equation from Klein-Gordon free particle’s wave function in cosmological special theory of relativity.

scholarly journals Klein-Gordon Equation and Wave Function in Cosmological Special Theory of Relativity

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Gordon Equation ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Klein Gordon ◽  
Klein Gordon Equation

In the Cosmological Special Theory of Relativity, we study energy-momentum relations, Klein-Gordon equation and wave function.

Special theory of relativity and the Sagnac effect

1988 ◽  
Vol 156 (9) ◽  
pp. 137-143 ◽  
Author(s):  
Anatolii A. Logunov ◽  
Yu.V. Chugreev
Keyword(s):  
Special Theory ◽  
Sagnac Effect ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

scholarly journals Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ituen B. Okon ◽  
E. Omugbe ◽  
Akaninyene D. Antia ◽  
C. A. Onate ◽  
Louis E. Akpabio ◽  
...  
Keyword(s):  
Dirac Equation ◽  
Thermodynamic Properties ◽  
Energy Equation ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Bound State ◽  
Compact Form ◽  
Relativistic Energy ◽  
Quadratic Potential ◽  
Special Cases

AbstractIn this research article, the modified approximation to the centrifugal barrier term is applied to solve an approximate bound state solutions of Dirac equation for spin and pseudospin symmetries with hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential using parametric Nikiforov–Uvarov method. The energy eigen equation and the unnormalised wave function were presented in closed and compact form. The nonrelativistic energy equation was obtain by applying nonrelativistic limit to the relativistic spin energy eigen equation. Numerical bound state energies were obtained for both the spin symmetry, pseudospin symmetry and the non relativistic energy. The screen parameter in the potential affects the solutions of the spin symmetry and non-relativistic energy in the same manner but in a revised form for the pseudospin symmetry energy equation. In order to ascertain the accuracy of the work, the numerical results obtained was compared to research work of existing literature and the results were found to be in excellent agreement to the existing literature. The partition function and other thermodynamic properties were obtained using the compact form of the nonrelativistic energy equation. The proposed potential model reduces to Hulthen and exponential inversely quadratic potential as special cases. All numerical computations were carried out using Maple 10.0 version and Matlab 9.0 version softwares respectively.

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