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 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.

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.

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 RELATIVISTIC BOUND STATES IN THE PRESENCE OF SPHERICALLY RING-SHAPED q-DEFORMED WOODS–SAXON POTENTIAL WITH ARBITRARY l-STATES

2013 ◽  
Vol 22 (03) ◽  
pp. 1350015 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
MAJID HAMZAVI ◽  
A. A. RAJABI
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Jacobi Polynomials ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Wave Functions ◽  
Potential Term ◽  
Component Wave ◽  
Relativistic Bound States ◽  
Potential Parameters

Approximate bound-state solutions of the Dirac equation with q-deformed Woods–Saxon (WS) plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary l-state. The energy eigenvalue equation and corresponding two-component wave functions are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov–Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term l(l+1)r-2. Under some limitations, we can obtain solution for the RS Hulthén potential and the standard usual spherical WS potential (q = 1).

Bhabha relativistic wave equations

1997 ◽  
Vol 30 (11) ◽  
pp. 4005-4017 ◽  
Author(s):  
R-K Loide ◽  
I Ots ◽  
R Saar
Keyword(s):  
Wave Equations ◽  
Relativistic Wave Equations ◽  
Relativistic Wave
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