scholarly journals Generalized relativistic wave equations with intrinsic maximum momentum

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
Chee Leong Ching ◽  
Wei Khim Ng
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Scalar Potential ◽  
Bound State ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Relativistic Wave ◽  
One Dimensional ◽  
Nonperturbative Effect ◽  
Klein Gordon

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein–Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.

scholarly journals l-state Solutions of the Relativistic and Non-Relativistic Wave Equations for Modified Hylleraas-Hulthen Potential Using the Nikiforov-Uvarov Quantum Formalism

2018 ◽  
Vol 3 (1) ◽  
pp. 03-09 ◽  
Author(s):  
Hitler Louis ◽  
Ita B. Iserom ◽  
Ozioma U. Akakuru ◽  
Nelson A. Nzeata-Ibe ◽  
Alexander I. Ikeuba ◽  
...  
Keyword(s):  
Wave Equations ◽  
Approximation Scheme ◽  
Jacobi Polynomials ◽  
Energy Eigenvalue ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Relativistic Wave ◽  
Type Approximation ◽  
Klein Gordon

An exact analytical and approximate solution of the relativistic and non-relativistic wave equations for central potentials has attracted enormous interest in recent years. By using the basic Nikiforov-Uvarov quantum mechanical concepts and formalism, the energy eigenvalue equations and the corresponding wave functions of the Klein–Gordon and Schrodinger equations with the interaction of Modified Hylleraas-Hulthen Potentials (MHHP) were obtained using the conventional Pekeris-type approximation scheme to the orbital centrifugal term. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals BOUND STATES OF THE KLEIN–GORDON EQUATION IN THE PRESENCE OF SHORT RANGE POTENTIALS

2006 ◽  
Vol 21 (02) ◽  
pp. 313-325 ◽  
Author(s):  
VÍCTOR M. VILLALBA ◽  
CLARA ROJAS
Keyword(s):  
Short Range ◽  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
One Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

scholarly journals Relativistic wave equations with fractional derivatives and pseudodifferential operators

2002 ◽  
Vol 2 (4) ◽  
pp. 163-197 ◽  
Author(s):  
Petr Závada
Keyword(s):  
Fractional Derivatives ◽  
Wave Equations ◽  
Pseudodifferential Operators ◽  
Relativistic Wave Equations ◽  
Green Functions ◽  
Relativistic Wave ◽  
Fractional Powers ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Symmetry Transformations

We study the class of the free relativistic covariant equations generated by the fractional powers of the d′Alembertian operator(□1/n). The equations corresponding ton=1and2(Klein-Gordon and Dirac equations) are local in their nature, but the multicomponent equations for arbitraryn>2are nonlocal. We show the representation of the generalized algebra of Pauli and Dirac matrices and how these matrices are related to the algebra ofSU (n)group. The corresponding representations of the Poincaré group and further symmetry transformations on the obtained equations are discussed. The construction of the related Green functions is suggested.

scholarly journals Scattering State of Klein-Gordon Particles by q-Parameter Hyperbolic Poschl-Teller Potential

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Akpan Ndem Ikot ◽  
Hillary P. Obong ◽  
Israel O. Owate ◽  
Michael C. Onyeaju ◽  
Hassan Hassanabadi
Keyword(s):  
Bound States ◽  
Hypergeometric Functions ◽  
Energy Equation ◽  
Bound State ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Scattering State ◽  
Klein Gordon ◽  
The One

The one-dimensional Klein-Gordon equation for equal vector and scalar q-parameter hyperbolic Poschl-Teller potential is solved in terms of the hypergeometric functions. We calculate in detail the solutions of the scattering and bound states. By virtue of the conditions of equation of continuity of the wave functions, we obtained explicit expressions for the reflection and transmission coefficients and energy equation for the bound state solutions.

Relativistic Wave Equations

2019 ◽  
pp. 25-42
Author(s):  
Michael E. Peskin
Keyword(s):  
Dirac Equation ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Relativistic Wave Equations ◽  
Quantum Mechanical ◽  
Relativistic Wave ◽  
Klein Gordon ◽  
Klein Gordon Equation

This chapter presents the wave equations that govern the behavior of quantum mechanical particles with spin 0, 1/2, and 1 in relativistic theories. These equations are the Klein-Gordon equation, the Dirac equation, and Maxwell’s equations.

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