III Time-dependent relativistic wave equations: Numerics of the Dirac and the Klein–Gordon equation

SPARK ◽  
2018 ◽  
Author(s):  
Heiko Bauke
Keyword(s):  
Wave Equations ◽  
Gordon Equation ◽  
Relativistic Wave Equations ◽  
Time Dependent ◽  
Relativistic Wave ◽  
Klein Gordon ◽  
Klein Gordon Equation

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.

Relativistic Wave Equations

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Dirac Equation ◽  
Vector Fields ◽  
Wave Equations ◽  
Gordon Equation ◽  
Relativistic Wave ◽  
Wave Solutions ◽  
Lagrangian Formulations ◽  
Klein Gordon ◽  
Conserved Currents ◽  
Klein Gordon Equation

Relativistically covariant wave equations for scalar, spinor, and vector fields. Plane wave solutions and Green’s functions. The Klein–Gordon equation. The Dirac equation and the Clifford algebra of γ‎ matrices. Symmetries and conserved currents. Hamiltonian and Lagrangian formulations. Wave equations for spin-1 fields.

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 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 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 Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Wave Equations ◽  
Gordon Equation ◽  
Space Time ◽  
Wave Functions ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Gauge Fixing ◽  
Klein Gordon ◽  
Klein Gordon Equation

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

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