2012, ISBN 9781848167971, xiii, 201

Book

REVIEWS IN MATHEMATICAL PHYSICS, ISSN 0129-055X, 10/2019, Volume 31, Issue 9, p. 1950032

The relativistic Lippmann-Schwinger equation was earlier formulated in terms of the limit values of the corresponding resolvent. In the present paper, we write...

scattering operator | Dirac equation | relativistic scattering amplitude | wave operator | compact operator | SCATTERING PROBLEMS | PHYSICS, MATHEMATICAL | relativistic Lippmann-Schwinger equation | Rollnik class

scattering operator | Dirac equation | relativistic scattering amplitude | wave operator | compact operator | SCATTERING PROBLEMS | PHYSICS, MATHEMATICAL | relativistic Lippmann-Schwinger equation | Rollnik class

Journal Article

1992, Texts and monographs in physics., ISBN 9783540548836, xvii, 357

Book

2007, Lecture notes in physics, ISBN 9783540712923, Volume 722, xiv, 445

Maxwell, Dirac and Einstein's equations are certainly among the most imp- tant equations of XXth century Physics and it is our intention in this book to 1...

Space and time | Geometry, Differential | Dirac equation | Relativity (Physics) | Maxwell equations | Mathematical physics | Einstein field equations | Mathematical Methods in Physics | Differential Geometry | Relativity and Cosmology | Physics

Space and time | Geometry, Differential | Dirac equation | Relativity (Physics) | Maxwell equations | Mathematical physics | Einstein field equations | Mathematical Methods in Physics | Differential Geometry | Relativity and Cosmology | Physics

Book

2015, 2nd edition., Advances in applied mathematics, ISBN 9781482251029, xvii, 667

Since publication of the first edition over a decade ago, Green's Functions with Applicationshas provided applied scientists and engineers with a systematic...

Green's functions | Green-Funktion

Green's functions | Green-Funktion

Book

1993, Mathematics, theory & applications., ISBN 9780817636814, xviii, 307

Book

Nature, ISSN 0028-0836, 01/2010, Volume 463, Issue 7277, pp. 68 - 71

The Dirac equation(1) successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the...

GRAPHENE | MULTIDISCIPLINARY SCIENCES | Models | Research | Simulation methods | Methods | Quantum theory | Dirac equation

GRAPHENE | MULTIDISCIPLINARY SCIENCES | Models | Research | Simulation methods | Methods | Quantum theory | Dirac equation

Journal Article

1997, 2nd rev. ed., ISBN 3540616217, xix, 424

Book

Nonlinear Dynamics, ISSN 0924-090X, 4/2017, Volume 88, Issue 2, pp. 1257 - 1271

The Darboux transformation (DT) for the super-integrable hierarchy has an essential difference from the general system. As we know, the super-integrable...

Super-Dirac equation | Engineering | Vibration, Dynamical Systems, Control | Super-Schrödinger equation | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Darboux transformation | Exact solution | SUPERSYMMETRIES | INTEGRABILITY | NONLINEAR-WAVES | SYMMETRIES | HARMONIC-OSCILLATOR | Super-Schrodinger equation | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | MECHANICS | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | OPERATOR | HIERARCHY | Inhomogeneous media | Transformations | Schroedinger equation | Hierarchies | Solitary waves | Dirac equation

Super-Dirac equation | Engineering | Vibration, Dynamical Systems, Control | Super-Schrödinger equation | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Darboux transformation | Exact solution | SUPERSYMMETRIES | INTEGRABILITY | NONLINEAR-WAVES | SYMMETRIES | HARMONIC-OSCILLATOR | Super-Schrodinger equation | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | MECHANICS | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | OPERATOR | HIERARCHY | Inhomogeneous media | Transformations | Schroedinger equation | Hierarchies | Solitary waves | Dirac equation

Journal Article

Journal of Mathematical Sciences, ISSN 1072-3374, 6/2018, Volume 231, Issue 6, pp. 820 - 826

The paper deals with nonlinear one-dimensional Dirac equation. We describe the set of its invariants by means of the deformed linear Dirac equation using the...

Mathematics, general | Mathematics | Differential equations | Research | Mathematics - Dynamical Systems | ONE-DIMENSIONAL CALCULATIONS | DIRAC EQUATION | NONLINEAR PROBLEMS | DEFORMATION | MATHEMATICAL METHODS AND COMPUTING

Mathematics, general | Mathematics | Differential equations | Research | Mathematics - Dynamical Systems | ONE-DIMENSIONAL CALCULATIONS | DIRAC EQUATION | NONLINEAR PROBLEMS | DEFORMATION | MATHEMATICAL METHODS AND COMPUTING

Journal Article

Physics Letters A, ISSN 0375-9601, 07/2017, Volume 381, Issue 25-26, pp. 2050 - 2054

New exact analytical bound-state solutions of the radial Dirac equation in dimensions for two sets of couplings and radial potential functions are obtained via...

Dirac equation | Morse potential | STEP-DOWN OPERATORS | LAPLACE TRANSFORM | STATES | PHYSICS, MULTIDISCIPLINARY | SINGULAR HARMONIC-OSCILLATOR | LADDER OPERATORS | PLUS

Dirac equation | Morse potential | STEP-DOWN OPERATORS | LAPLACE TRANSFORM | STATES | PHYSICS, MULTIDISCIPLINARY | SINGULAR HARMONIC-OSCILLATOR | LADDER OPERATORS | PLUS

Journal Article

1987, Mathematics and its applications. (Soviet series), ISBN 9789027723208, Volume MASS8., xiv, 214

Book

New Journal of Physics, ISSN 1367-2630, 2014, Volume 16, Issue 9, pp. 93008 - 25

We write the charge-free Maxwell equations in a form analogous to that of the Dirac equation for a free electron. This allows us to apply to light some of the...

optical angular momentum | relativistic quantum theory | mechanical properties of light | Dirac equation | SPIN | PHYSICS, MULTIDISCIPLINARY | LIGHT | ELECTROMAGNETIC-FIELD | CONSERVATION LAW | PARTICLE ASPECT | ORBITAL ANGULAR-MOMENTUM | MAXWELL | WAVE-EQUATION | Relativistic theory | Orbitals | Free electrons | Maxwell equation

optical angular momentum | relativistic quantum theory | mechanical properties of light | Dirac equation | SPIN | PHYSICS, MULTIDISCIPLINARY | LIGHT | ELECTROMAGNETIC-FIELD | CONSERVATION LAW | PARTICLE ASPECT | ORBITAL ANGULAR-MOMENTUM | MAXWELL | WAVE-EQUATION | Relativistic theory | Orbitals | Free electrons | Maxwell equation

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 02/2015, Volume 142, Issue 8, p. 084117

The free-complement (FC) method is a general method for solving the Schrodinger equation (SE): The produced wave function has the potentially exact structure...

MATRIX RENORMALIZATION-GROUP | ITERATIVE CONFIGURATION-INTERACTION | GROUND-STATE | COLLOCATION METHOD | DIRAC EQUATIONS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | VIBRATIONAL BOUND-STATES | HYDROGEN-ATOM | EXACT WAVE-FUNCTION | ELECTRONIC-STRUCTURE | EXCITED-STATES | Quantum Theory | Models, Chemical | Hydrogen - chemistry | Helium - chemistry | Schroedinger equation | Helium | Sampling | Integrals | INTEGRALS | HYDROGEN | MATHEMATICAL SOLUTIONS | SAMPLING | SCHROEDINGER EQUATION | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY | ATOMS | POTENTIALS | COMPARATIVE EVALUATIONS | HELIUM | VARIATIONAL METHODS | MOLECULES

MATRIX RENORMALIZATION-GROUP | ITERATIVE CONFIGURATION-INTERACTION | GROUND-STATE | COLLOCATION METHOD | DIRAC EQUATIONS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | VIBRATIONAL BOUND-STATES | HYDROGEN-ATOM | EXACT WAVE-FUNCTION | ELECTRONIC-STRUCTURE | EXCITED-STATES | Quantum Theory | Models, Chemical | Hydrogen - chemistry | Helium - chemistry | Schroedinger equation | Helium | Sampling | Integrals | INTEGRALS | HYDROGEN | MATHEMATICAL SOLUTIONS | SAMPLING | SCHROEDINGER EQUATION | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY | ATOMS | POTENTIALS | COMPARATIVE EVALUATIONS | HELIUM | VARIATIONAL METHODS | MOLECULES

Journal Article

EPL, ISSN 0295-5075, 11/2016, Volume 116, Issue 4, pp. 40001 - 40001

Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the...

PHYSICS, MULTIDISCIPLINARY | ELECTRON | MODEL | Mathematical analysis | Dirac equation | Exact solutions | Eigenvalues | Oscillations | Wave functions | Tachyons | Strings

PHYSICS, MULTIDISCIPLINARY | ELECTRON | MODEL | Mathematical analysis | Dirac equation | Exact solutions | Eigenvalues | Oscillations | Wave functions | Tachyons | Strings

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 7287 - 7306

In this paper, we introduce a q‐analog of 1‐dimensional Dirac equation. We investigate the existence and uniqueness of the solution of this equation. Later, we...

q−Dirac operator | self‐adjoint operator | Green matrix | eigenfunction expansions | eigenvalues and eigenfunctions | Eigenfunction expansions | Self-adjoint operator | Eigenvalues and eigenfunctions | Q−Dirac operator | self-adjoint operator | POLYNOMIALS | MATHEMATICS, APPLIED | q-Dirac operator | Eigenvalues | Eigenvectors | Green's functions | Orthogonality | Dirac equation | Uniqueness

q−Dirac operator | self‐adjoint operator | Green matrix | eigenfunction expansions | eigenvalues and eigenfunctions | Eigenfunction expansions | Self-adjoint operator | Eigenvalues and eigenfunctions | Q−Dirac operator | self-adjoint operator | POLYNOMIALS | MATHEMATICS, APPLIED | q-Dirac operator | Eigenvalues | Eigenvectors | Green's functions | Orthogonality | Dirac equation | Uniqueness

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2014, Volume 256, pp. 728 - 747

A finite difference scheme is presented for the Dirac equation in D. It can handle space- and time-dependent mass and potential terms and utilizes exact...

Finite difference | Fermion doubling | Leap-frog | Dirac equation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ELECTRONS | SCHRODINGER-EQUATION | DYNAMICS | Leap frog | SYSTEMS | MODEL | PHYSICS, MATHEMATICAL | Mathematical analysis | Norms | Boundary conditions | Reflection | Dispersions | Boundaries | Finite difference method | Fermions | Preserves

Finite difference | Fermion doubling | Leap-frog | Dirac equation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ELECTRONS | SCHRODINGER-EQUATION | DYNAMICS | Leap frog | SYSTEMS | MODEL | PHYSICS, MATHEMATICAL | Mathematical analysis | Norms | Boundary conditions | Reflection | Dispersions | Boundaries | Finite difference method | Fermions | Preserves

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 06/2017, Volume 27, Issue 2, pp. 1779 - 1799

Using Clifford and Spin-Clifford formalisms we prove that the classical relativistic Hamilton Jacobi equation for a charged massive (and spinning) particle...

Clifford bundle | Hamilton–Jacobi equation | de Broglie–Bohm theory | Dirac equation | FIELDS | MATHEMATICS, APPLIED | Hamilton-Jacobi equation | SPINOR-STRUCTURE | GENERAL-RELATIVITY | OBSERVABLES | de Broglie-Bohm theory | PHYSICS, MATHEMATICAL | SPACE-TIMES | Electromagnetic fields | Electromagnetism

Clifford bundle | Hamilton–Jacobi equation | de Broglie–Bohm theory | Dirac equation | FIELDS | MATHEMATICS, APPLIED | Hamilton-Jacobi equation | SPINOR-STRUCTURE | GENERAL-RELATIVITY | OBSERVABLES | de Broglie-Bohm theory | PHYSICS, MATHEMATICAL | SPACE-TIMES | Electromagnetic fields | Electromagnetism

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 07/2017, Volume 140, pp. 1010 - 1019

We have shown that the quantum Telegraph equation (QTE) is a quantum equation for the description of quantum phenomena. It inherently embodies the...

Schrodinger equation | De broglie wave equation | Quantum mechanics | Dirac equation | Telegraph equation | Matter wave equation | Klein–Gordon equation | Bohmian quantum mechanics | Klein-Gordon equation | DIFFRACTION | OPTICS | Electrical conductivity

Schrodinger equation | De broglie wave equation | Quantum mechanics | Dirac equation | Telegraph equation | Matter wave equation | Klein–Gordon equation | Bohmian quantum mechanics | Klein-Gordon equation | DIFFRACTION | OPTICS | Electrical conductivity

Journal Article

Physical Review Letters, ISSN 0031-9007, 12/2018, Volume 121, Issue 25, p. 253202

A semirelativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that...

PHYSICS, MULTIDISCIPLINARY | Time dependence | Ultraviolet lasers | Propagation | Lasers | Dirac equation | Relativism | Relativistic velocity | Schroedinger equation | Relativistic effects | Electronic excitations | Multiphoton tunneling ionizations | Strong electromagnetic field effects | Relativistic, quantum, electrodynamic effects | Light-matter interactions | Atomic processes | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

PHYSICS, MULTIDISCIPLINARY | Time dependence | Ultraviolet lasers | Propagation | Lasers | Dirac equation | Relativism | Relativistic velocity | Schroedinger equation | Relativistic effects | Electronic excitations | Multiphoton tunneling ionizations | Strong electromagnetic field effects | Relativistic, quantum, electrodynamic effects | Light-matter interactions | Atomic processes | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

Journal Article