Massless fermion quasinormal modes in the Horava–Lifshitz background

2013 ◽  
Vol 91 (3) ◽  
pp. 251-255 ◽  
Author(s):  
J. Sadeghi ◽  
B. Pourhassan ◽  
K. Jafarzadeh ◽  
E. Reisi ◽  
M. Rostami
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Quasinormal Modes ◽  
Factorization Method ◽  
Massless Fermion

In this paper we consider the Horava–Lifshitz background and obtain the massless fermion quasinormal modes. In that case we use the Newman–Penrose formalism and the massless Dirac equation to calculate the radial and angular parts of equations. The wave function and corresponding modes can be obtained using the factorization method.

A solvable two-body Dirac equation in one space dimension

1991 ◽  
Vol 69 (7) ◽  
pp. 780-785 ◽  
Author(s):  
F. Dominguez-Adame ◽  
B. Méndez
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Space Dimension ◽  
Translational Motion ◽  
Effective Frequency ◽  
Klein Paradox ◽  
Independent Components ◽  
Dirac Particles ◽  
One Space Dimension

A solvable Hamiltonian for two Dirac particles interacting by instantaneous linear potentials in (1 + 1) dimensions is discussed. The system presents no Klein paradox even if the coupling is rather strong, so particles remain bound. The four independent components of the wave function describing the system resemble the nonrelativistic oscillator eigenfunctions. Although the Hamiltonian is not fully covariant, the effective frequency of the oscillator obeys a typical relativistic Doppler law. In contrast to the nonrelativistic treatment, eigenstates are intrinsically coupled with the overall translational motion of the system.

scholarly journals Dirac Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Dirac Equation ◽  
Inertial Frame ◽  
Gordon Equation ◽  
Probability Amplitude ◽  
Function Type ◽  
Klein Gordon ◽  
Klein Gordon Equation

Dirac equation is a one order-wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Dirac Equation from wave function, Type A in cosmological inertial frame.The Dirac equation satisfy Klein-Gordon equation in cosmological inertial frame.

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.

Effect of the Wigner–Dunkl algebra on the Dirac equation and Dirac harmonic oscillator

2018 ◽  
Vol 33 (25) ◽  
pp. 1850146 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Functional Analysis ◽  
Wave Function ◽  
Dirac Equation ◽  
Harmonic Oscillator ◽  
Limit State ◽  
Energy Eigenvalue ◽  
Eigenvalue Equation ◽  
Reflection Symmetry ◽  
Analysis Method ◽  
One Dimensional

In this work, we study the Dirac equation and Dirac harmonic oscillator in one-dimensional via the Dunkl algebra. By using Dunkl derivative, we solve the momentum operator and Hamiltonian that include the reflection symmetry. Based on the concept of the Wigner–Dunkl algebra and the functional analysis method, we have obtained the energy eigenvalue equation and the corresponding wave function for Dirac harmonic oscillator and Dirac equation, respectively. It is shown all results in the limit state satisfied what we had expected before.

scholarly journals Factorization Method in Oscillator with the Aharonov-Casher System

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
J. Sadeghi ◽  
Jalil Naji ◽  
Behnam Pourhassan
Keyword(s):  
Wave Function ◽  
Energy Spectrum ◽  
Factorization Method ◽  
Mathematical Foundation ◽  
Raising And Lowering Operators ◽  
General Wave ◽  
Lowering Operators

We review the oscillator with Aharonov-Casher system and study some mathematical foundation about factorization method. The factorization method helps us to obtain the energy spectrum and general wave function for the corresponding system in some spin condition. The factorization method leads us to obtain the raising and lowering operators for the Aharonov-Casher system. The corresponding operators give us the generators of the algebra.

scholarly journals Fermion clouds around z = 0 Lifshitz black holes

2020 ◽  
Vol 17 (09) ◽  
pp. 2050143
Author(s):  
Gülni̇hal Tokgöz ◽  
İzzet Sakallı
Keyword(s):  
Boundary Condition ◽  
Dirac Equation ◽  
Bessel Functions ◽  
Dirichlet Boundary ◽  
Quasinormal Modes ◽  
Wave Condition ◽  
Spheroidal Harmonics ◽  
Lifshitz Black Holes ◽  
Lifshitz Black Hole ◽  
Area Spectra

In this work, the Dirac equation is studied in the [Formula: see text] Lifshitz black hole ([Formula: see text]LBH) spacetime. The set of equations representing the Dirac equation in the Newman–Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which are independent of mass, is reduced to Zerilli equations (ZEs) with their associated potentials. In the near horizon (NH) region, these equations are solved in terms of the Bessel functions of the first and second kinds arising from the fermionic perturbation on the background geometry. For computing the boxed quasinormal modes (BQNMs) instead of the ordinary quasinormal modes (QNMs), we first impose the purely ingoing wave condition at the event horizon. Then, Dirichlet boundary condition (DBC) and Newmann boundary condition (NBC) are applied in order to get the resonance conditions. For solving the resonance conditions, we follow the Hod’s iteration method. Finally, Maggiore’s method (MM) is employed to derive the entropy/area spectra of the [Formula: see text]LBH which are shown to be equidistant.

Rigorous wave function for spin- composite particles

1968 ◽  
Vol 46 (7) ◽  
pp. 909-909
Author(s):  
Gerald Rosen
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Composite Particles ◽  
Spinor Wave Function ◽  
Relativistic Spin ◽  
Spinor Wave

A certain composite four-index quantity built up from three constituent spinor wave function solutions to the Dirac equation is shown to transform as a spinor and to satisfy the Dirac equation. This rigorous wave function is therefore associated with a composite relativistic spin-[Formula: see text] particle.

scholarly journals A SIMPLE DIRAC WAVE FUNCTION FOR A COULOMB POTENTIAL WITH LINEAR CONFINEMENT

1999 ◽  
Vol 14 (34) ◽  
pp. 2409-2411 ◽  
Author(s):  
JERROLD FRANKLIN
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Dirac Equation ◽  
Coulomb Potential ◽  
Ground State ◽  
Linear Potential ◽  
Confining Potential ◽  
Lorentz Scalar ◽  
Dirac Wave Function ◽  
Scalar Part

A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part dominating, can be chosen to give a simple Dirac wave function. The binding energy depends only on the Coulomb strength and is not affected by the linear potential. The method works for the ground state, or for the lowest state with l=j-1/2, for any j.

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.

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