Quantum-mechanical two-center problem for the Dirac equation

1976 ◽  
Vol 28 (2) ◽  
pp. 737-744 ◽  
Author(s):  
V. A. Lyul'ka
Keyword(s):  
Dirac Equation ◽  
Quantum Mechanical ◽  
Center Problem

Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation

2016 ◽  
Vol 71 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Friedwardt Winterberg
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Negative Energy ◽  
Quantum Mechanical ◽  
Field Equations ◽  
Negative Mass ◽  
Pilot Wave ◽  
Extended Theories Of Gravity

AbstractAn explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein’s gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive–negative mass (pole–dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal “Zitterbewegung” (quivering motion), emitting a watt-less oscillating positive–negative space curvature wave. It is shown that this thusly produced “Zitterbewegung” reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie’s pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.

THE SOLUTION OF DIRAC EQUATION IN QUASI-EXTREME REISSNER–NORDSTRÖM DE SITTER SPACE

2009 ◽  
Vol 24 (30) ◽  
pp. 2433-2443 ◽  
Author(s):  
YAN LYU ◽  
SONG CUI ◽  
LING LIU
Keyword(s):  
Dirac Equation ◽  
Inverse Function ◽  
Quantum Mechanical ◽  
De Sitter ◽  
Mechanical Method ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
First Case ◽  
Quantum Mechanical Method ◽  
Tortoise Coordinate

The radial parts of Dirac equation between the outer black hole horizon and the cosmological horizon in quasi-extreme Reissner–Nordström de Sitter (RNdS) geometry is solved numerically. We use an accurate polynomial approximation to mimic the modified tortoise coordinate [Formula: see text], for obtaining the inverse function [Formula: see text] and [Formula: see text]. We then use a quantum mechanical method to solve the wave equation and give the reflection and transmission coefficients. We concentrate on two limiting cases. The first case is when the two horizons are close to each other, and the second case is when the horizons are far apart.

scholarly journals Generalized quantum mechanical two-Coulomb-center problem (Demkov problem)

2013 ◽  
Vol 22 (9) ◽  
pp. 090306 ◽  
Author(s):  
A. M. Puchkov ◽  
A. V. Kozedub ◽  
E. O. Bodnia
Keyword(s):  
Quantum Mechanical ◽  
Center Problem ◽  
Coulomb Center

scholarly journals The Illusion of Quantum Mechanical Probability Waves

2020 ◽  
Vol 5 (10) ◽  
pp. 1212-1224
Author(s):  
Wim Vegt
Keyword(s):  
Wave Equation ◽  
Dirac Equation ◽  
Electromagnetic Waves ◽  
Quantum Physics ◽  
Probability Function ◽  
Relativistic Quantum ◽  
Science And Religion ◽  
Niels Bohr ◽  
Quantum Mechanical ◽  
Mechanical Probability

An important milestone in quantum physics has been reached by the publication of the Relativistic Quantum Mechanical Dirac Equation in 1928. However, the Dirac equation represents a 1-Dimensional quantum mechanical equation which is unable to describe the 4-Dimensional Physical Reality. In this article the 4-Dimensional Relativistic Quantum Mechanical Dirac Equation expressed in the vector probability functions  and the complex conjugated vector probability function  will be published. To realize this, the classical boundaries of physics has to be changed. It is necessary to go back in time 300 years ago. More than 200 years ago before the Dirac Equation had been published. A Return to the Inception of Physics. The time of Isaac Newton who published in 1687 in the “Philosophiae Naturalis Principia Mathematica” a Universal Fundamental Principle in Physics which was in Harmony with Science and Religion. The Universal Path, the Leitmotiv, the Universal Concept in Physics. Newton found the concept of “Universal Equilibrium” which he formulated in his famous third equation Action = - Reaction. This article presents a New Kind of Physics based on this Universal Fundamental Concept in Physics which results in a New Approach in Quantum Physics and General Relativity. The physical concept of quantum mechanical probability waves has been created during the famous 1927 5th Solvay Conference. During that period there were several circumstances which came together and made it possible to create an unique idea of material waves being complex (partly real and partly imaginary) and describing the probability of the appearance of a physical object (elementary particle). The idea of complex probability waves was new in the beginning of the 20th century. Since then the New Concept has been protected carefully within the Copenhagen Interpretation. When Schrödinger published his famous material wave equation in 1926, he found spherical and elliptical solutions for the presence of the electron within the atom. The first idea of the material waves in Schrödinger’s wave equation was the concept of confined Electromagnetic Waves. But according to Maxwell this was impossible. According to Maxwell’s equations Electromagnetic Waves can only propagate along straight lines and it is impossible that Light (Electromagnetic Waves) could confine with the surface of a sphere or an ellipse. For that reason, these material waves in Schrödinger’s wave equation could only be of a different origin than Electromagnetic Waves. Niels Bohr introduced the concept of “Probability Waves” as the origin of the material waves in Schrödinger’s wave equation. And defined the New Concept that the electron was still a particle but the physical presence of the electron in the Atom was equally divided by a spherical probability function. In the New Theory it will be demonstrated that because of a mistake in the Maxwell Equations, in 1927 Confined Electromagnetic waves could not be considered to be the material waves expressed in Schrödinger's wave equation. The New Theory presents a new equation describing electromagnetic field configurations which are also solutions of the Schrodinger's wave equation and the relativistic quantum mechanical Dirac Equation and carry mass, electric charge and magnetic spin at discrete values.

TWO-CENTER PROBLEM FOR THE DIRAC EQUATION WITH A COULOMB AND SCALAR POTENTIAL

2007 ◽  
Vol 22 (18) ◽  
pp. 3123-3130
Author(s):  
V. V. BONDARCHUK ◽  
I. M. SHVAB ◽  
A. V. KATERNOGA
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Ground State ◽  
Scalar Potential ◽  
Scalar Coupling ◽  
Center Problem ◽  
Energy Term ◽  
Coupling Constant ◽  
Scalar Coupling Constant ◽  
Scalar Potentials

The ground state wave function and the energy term of a relativistic electron moving in the field of two fixed centers, when interaction of this particle with centers is described by two Coulomb and two Coulomb-like scalar potentials are calculated analytically by the LCAO method. Dependence of electron binding energy from value of scalar coupling constant was investigated using obtained analytic results.

The WKB method for the quantum mechanical two-Coulomb-center problem

2017 ◽  
Vol 190 (3) ◽  
pp. 345-358 ◽  
Author(s):  
M. Hnatich ◽  
V. M. Khmara ◽  
V. Yu. Lazur ◽  
O. K. Reity
Keyword(s):  
Quantum Mechanical ◽  
Wkb Method ◽  
Center Problem ◽  
Coulomb Center

AN APPROXIMATE SOLUTION OF THE DIRAC EQUATION FOR HYPERBOLIC SCALAR AND VECTOR POTENTIALS AND A COULOMB TENSOR INTERACTION BY SUSYQM

2011 ◽  
Vol 26 (36) ◽  
pp. 2703-2718 ◽  
Author(s):  
H. HASSANABADI ◽  
E. MAGHSOODI ◽  
S. ZARRINKAMAR ◽  
H. RAHIMOV
Keyword(s):  
Approximate Solution ◽  
Dirac Equation ◽  
Significant Role ◽  
Tensor Interaction ◽  
Nuclear Spectroscopy ◽  
Quantum Mechanical ◽  
Vector Potentials ◽  
Analytical Scheme ◽  
Hyperbolic Form

Based on the significant role of spin and pseudospin symmetries in hadron and nuclear spectroscopy, we have investigated Dirac equation under scalar and vector potentials of cotangent hyperbolic form besides a Coulomb tensor interaction via an approximate analytical scheme. The considered potential for small potential parameter resembles the well-established Kratzer potential. In addition, we see how the tensor term removes the degeneracy of doublets. After an acceptable approximation, namely a Pekeris-type one, we see that the problem is simply solved via the quantum mechanical idea of supersymmetry without having to deal with the cumbersome, complicated and time-consuming numerical programming.

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