Relativistic quantum bouncing particles in a homogeneous gravitational field

2021 ◽  
pp. 2150098
Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin
Keyword(s):  
Gravitational Field ◽  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Dirac Equations ◽  
Rindler Coordinates ◽  
Klein Gordon ◽  
Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

Calculation of the energy levels and charge radius of 24Mg and 32S isotopes in the cluster model

2020 ◽  
Vol 98 (2) ◽  
pp. 148-152
Author(s):  
Sahar Aslanzadeh ◽  
Mohammad Reza Shojaei ◽  
Ali Asghar Mowlavi
Keyword(s):  
Experimental Data ◽  
Excited State ◽  
Cluster Model ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Alpha Particles ◽  
Wave Functions ◽  
S Isotopes ◽  
Klein Gordon ◽  
Nu Method

In this work, the 24Mg and 32S isotopes are considered in the cluster model by solving the Schrödinger and Klein–Gordon equations using the Nikiforov–Uvarov (NU) method. The configuration of the alpha particles for the second excited state for 24Mg isotope is 12C + 12C. A local potential is used for these two equations that is compatible to the modified Hulthen plus quadratic Yukawa potential. By substituting this potential in the Schrödinger and Klein–Gordon equations, the energy levels and wave functions are obtained. The calculated results from the Schrödinger and Klein–Gordon equations, i.e., nonrelativity and relativity, respectively, are close to the results from experimental data.

scholarly journals Toward a quantum theory of tachyon fields

2016 ◽  
Vol 31 (09) ◽  
pp. 1650041 ◽  
Author(s):  
Charles Schwartz
Keyword(s):  
Quantum Theory ◽  
Mass Shell ◽  
Group Representation ◽  
Lorentz Invariance ◽  
Critical Role ◽  
Wave Functions ◽  
Time Points ◽  
Dirac Equations ◽  
Consistent Manner ◽  
Klein Gordon

We construct momentum space expansions for the wave functions that solve the Klein–Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space–time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.

scholarly journals Spin-0 scalar particle interacts with scalar potential in the presence of magnetic field and quantum flux under the effects of KKT in 5D cosmic string spacetime

2020 ◽  
pp. 2150004
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Magnetic Field ◽  
Quantum Dynamics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Klein Theory ◽  
Klein Gordon ◽  
Quantum Flux

In this paper, we study a relativistic quantum dynamics of spin-0 scalar particle interacts with scalar potential in the presence of a uniform magnetic field and quantum flux in background of Kaluza–Klein theory (KKT). We solve Klein–Gordon equation in the considered framework and analyze the relativistic analogue of the Aharonov–Bohm effect for bound states. We show that the energy levels depend on the global parameters characterizing the spacetime, scalar potential and the magnetic field which break their degeneracy.

scholarly journals NONCOMMUTATIVE SPACE CORRECTIONS ON THE KLEIN–GORDON AND DIRAC OSCILLATORS SPECTRA

2011 ◽  
Vol 26 (29) ◽  
pp. 4991-5003 ◽  
Author(s):  
ROBERTO V. MALUF
Keyword(s):  
Perturbation Theory ◽  
Energy Levels ◽  
Zeeman Splitting ◽  
Nonrelativistic Limit ◽  
Order Perturbation ◽  
Noncommutative Space ◽  
First Order ◽  
Commutative Space ◽  
Klein Gordon ◽  
First Order Perturbation

We consider the influence of a noncommutative space on the Klein–Gordon and the Dirac oscillators. The nonrelativistic limit is taken and the θ-modified Hamiltonians are determined. The corrections of these Hamiltonians on the energy levels are evaluated in first-order perturbation theory. It is observed a total lifting of the degeneracy to the considered levels. Such effects are similar to the Zeeman splitting in a commutative space.

scholarly journals Three-Dimensional Dirac Oscillator with Minimal Length: Novel Phenomena for Quantized Energy

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Malika Betrouche ◽  
Mustapha Maamache ◽  
Jeong Ryeol Choi
Keyword(s):  
Energy Spectrum ◽  
Energy Levels ◽  
Three Dimensional ◽  
Nonrelativistic Limit ◽  
Minimal Length ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Planck Length ◽  
Standard Case ◽  
Small Parameters

We study quantum features of the Dirac oscillator under the condition that the position and the momentum operators obey generalized commutationrelations that lead to the appearance of minimal length with the order of the Planck length,∆xmin=ℏ3β+β′, whereβandβ′are two positive small parameters. Wave functions of the system and the corresponding energy spectrum are derived rigorously. The presence of the minimal length accompanies a quadratic dependence of the energy spectrum on quantum numbern, implying the property of hard confinement of the system. It is shown that the infinite degeneracy of energy levels appearing in the usual Dirac oscillator is vanished by the presence of the minimal length so long asβ≠0. Not only in the nonrelativistic limit but also in the limit of the standard case(β=β′=0), our results reduce to well known usual ones.

Relativistic quantum motion of spin-0 particles with a Cornell-type potential in (1 + 2)-dimensional Gürses spacetime backgrounds

2019 ◽  
Vol 34 (38) ◽  
pp. 1950314 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Quantum Dynamics ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Scalar Potential ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Quantum Motion ◽  
Type Potential ◽  
Klein Gordon Equation

In this work, we investigate the relativistic quantum dynamics of spin-0 particles in the background of (1 + 2)-dimensional Gürses spacetime [M. Gürses, Class. Quantum Grav. 11, 2585 (1994)] with interactions. We solve the Klein–Gordon equation subject to Cornell-type scalar potential in the considered framework, and evaluate the energy eigenvalues and corresponding wave functions, in detail.

scholarly journals Effects of extended uncertainty principle on the relativistic Coulomb potential

2021 ◽  
Vol 36 (03) ◽  
pp. 2150018
Author(s):  
B. Hamil ◽  
M. Merad ◽  
T. Birkandan
Keyword(s):  
Uncertainty Principle ◽  
Coulomb Potential ◽  
State Energy ◽  
Bound State ◽  
Wave Functions ◽  
De Sitter ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Relativistic Coulomb ◽  
Extended Uncertainty

The relativistic bound-state energy spectrum and the wave functions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein–Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.

Towards a Relativistic Quantum Mechanics

2021 ◽  
pp. 191-206
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Dirac Equation ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Negative Energy ◽  
Relativistic Quantum Mechanics ◽  
Quantum Field ◽  
Dirac Equations ◽  
Low Energies ◽  
Klein Gordon ◽  
Conserved Current

The Klein–Gordon and the Dirac equations are studied as candidates for a relativistic generalisation of the Schrödinger equation. We show that the first is unacceptable because it admits solutions with arbitrarily large negative energy and has no conserved current with positive definite probability density. The Dirac equation on the other hand does have a physically acceptable conserved current, but it too suffers from the presence of negative energy solutions. We show that the latter can be interpreted as describing anti-particles. In either case there is no fully consistent interpretation as a single-particle wave equation and we are led to a formalism admitting an infinite number of degrees of freedom, that is a quantum field theory. We can still use the Dirac equation at low energies when the effects of anti-particles are negligible and we study applications in atomic physics.

scholarly journals Relativistic and nonrelativistic solutions of the generalized Pöschl–Teller and hyperbolical potentials with some thermodynamic properties

2015 ◽  
Vol 24 (03) ◽  
pp. 1550020 ◽  
Author(s):  
C. A. Onate ◽  
J. O. Ojonubah
Keyword(s):  
Dirac Equation ◽  
Thermodynamic Properties ◽  
Hypergeometric Functions ◽  
Energy Equation ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Approximation Type ◽  
Supersymmetric Approach

By using the new approximation type, the Dirac equation is solved with the combination of Generalized Pöschl–Teller and Hyperbolical potentials within the framework of supersymmetric approach. The energy levels are obtained for both pseudospin and spin symmetries and the nonrelativistic limit is obtained with the corresponding wave functions in terms of hypergeometric functions. Some thermodynamic properties are equally obtained with the energy equation of the nonrelativistic limit.

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