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ISBN: 1470476274 Year: 2023 Publisher: Providence, RI : American Mathematical Society,
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ISBN: 1470420309 Year: 2014 Publisher: Providence, Rhode Island : American Mathematical Society,
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The Hamiltonian int_X(lvert{partial_t u}vert^2 + lvert{abla u}vert^2 + mathbf{m}^2lvert{u}vert^2),dx, defined on functions on mathbb{R}imes X, where X is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of u. The associated PDE is then a quasi-linear Klein-Gordon equation. The author shows that, when X is the sphere, and when the mass parameter mathbf{m} is outside an exceptional subset of zero measure, smooth Cauchy data of small size epsilon give rise to almost global solutions, i.e. solutions defined on a time interval of length c_Nepsilon^{-N} for any N. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on u) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus.
Hamiltonian systems. --- Klein-Gordon equation. --- Wave equation. --- Sphere.
Book
ISSN: 03031179 ISBN: 9782856293355 Year: 2012 Publisher: Paris Société mathématique de France
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ISBN: 9781470409838 Year: 2014 Publisher: Providence, Rhode Island : American Mathematical Society,
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Hamiltonian systems. --- Klein-Gordon equation. --- Wave equation. --- Sphere. --- Systèmes hamiltoniens --- Klein-Gordon, Equation de --- Equation d'onde --- Sphère
ISBN: 3540509860 0387509860 3662026341 9783540509868 9780387509860 354057266X 9783540572664 038757266X 9780387572666 Year: 1990 Volume: 3 Publisher: Berlin: Springer,
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Quantum mechanics. Quantumfield theory --- Wave equation --- Wave mechanics --- Théorie quantique des champs --- Equation d'onde --- Mécanique ondulatoire --- Klein-Gordon equation. --- Dirac equation. --- Relativistic quantum theory. --- 530.145.6 --- -Dirac equation --- Klein-Gordon equation --- Relativistic quantum theory --- Relativistic quantum mechanics --- Schrödinger-Klein-Gordon equation --- Wave mechanics. Corpuscular waves. Matrices --- 530.145.6 Wave mechanics. Corpuscular waves. Matrices --- Mécanique ondulatoire --- Mathematical physics --- #KVIV:BB --- #WSCH:AAS2 --- Quantum theory --- Special relativity (Physics) --- Quantum field theory --- Differential equations, Partial --- Physical mathematics --- Physics --- Problems, exercises, etc --- Mathematics --- Problems, exercises, etc. --- Particles (Nuclear physics) --- Physique mathématique --- Particules (Physique nucléaire) --- Théorie quantique des champs --- Dirac equation --- Mathematical physics - Problems, exercises, etc. --- Klein-gordon equation
ISBN: 3540674578 3662042754 Year: 2000 Publisher: Berlin Springer
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Relativistic Quantum Mechanics - Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. The first chapter deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties, and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-centre Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner) are also presented. The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course. This third edition has been slightly revised to bring the text up-to-date.
Dirac equation. --- Klein-Gordon equation. --- Relativistic quantum theory. --- Quantum mechanics. Quantumfield theory --- Klein-Gordon, Equation de --- Dirac, Equation de --- Théorie quantique relativiste --- Quantum theory. --- Quantum Physics. --- Particle and Nuclear Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Quantum physics. --- Nuclear physics. --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom
ISBN: 3662034255 3540616217 Year: 1997 Publisher: Berlin : Springer,
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Relativistic Quantum Mechanics - Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course.
Klein-Gordon equation. --- Dirac equation. --- Relativistic quantum theory. --- 530.145.6 --- Mathematical physics --- -Dirac equation --- Klein-Gordon equation --- Relativistic quantum theory --- #KVIV:BB --- #WSCH:AAS2 --- #dd Sabbe Camiel cfx --- Relativistic quantum mechanics --- Schrödinger-Klein-Gordon equation --- Physical mathematics --- Physics --- 530.145.6 Wave mechanics. Corpuscular waves. Matrices --- Wave mechanics. Corpuscular waves. Matrices --- Problems, exercises, etc --- Mathematics --- Dirac equation --- Dirac, Equation de --- Klein-Gordon, Equation de --- Théorie quantique relativiste --- Quantum theory --- Special relativity (Physics) --- Quantum field theory --- Wave equation --- Differential equations, Partial --- Quantum physics. --- Quantum computers. --- Spintronics. --- Quantum Physics. --- Quantum Information Technology, Spintronics. --- Fluxtronics --- Magnetoelectronics --- Spin electronics --- Spinelectronics --- Microelectronics --- Nanotechnology --- Computers --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Computer software --- Computer software. --- Development. --- Software, Computer --- Computer systems --- Development of computer software --- Software development
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ISBN: 0471906506 0471105090 9780471105091 9780471906506 Year: 1984 Publisher: Chichester: Wiley,
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Quantum mechanics. Quantumfield theory --- 530.145 --- #WSCH:AAS2 --- Quantum theory --- Quantum field theory. --- Physics --- Quantum field theory --- 530.145 Quantum theory --- $ Weak interactions(Leptonic-) --- $ Quantum electrodynamics(Radiative Corrections) --- $ Feynman graphs --- $ Scattering matrix expansion --- $ Electroweak interactions(Standard Model) --- $ Quantum electrodynamics(Regularization) --- $ Weak interactions(Gauge Theories) --- $ Quantum electrodynamics --- $ Quantum field theory --- $ Symmetry breaking in particle physics --- $ Photon covariant theory --- $ Dirac's theory --- $ Klein Gordon equation --- Théorie quantique des champs --- Weak interactions(Leptonic-) --- Quantum electrodynamics(Radiative Corrections) --- Feynman graphs --- Scattering matrix expansion --- Electroweak interactions(Standard Model) --- Quantum electrodynamics(Regularization) --- Weak interactions(Gauge Theories) --- Quantum electrodynamics --- Symmetry breaking in particle physics --- Photon covariant theory --- Dirac's theory --- Klein Gordon equation
Book
Year: 2021 Publisher: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute
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This book collects contributions to the Special Issue entitled "Symmetries in Quantum Mechanics and Statistical Physics" of the journal Symmetry. These contributions focus on recent advancements in the study of PT–invariance of non-Hermitian Hamiltonians, the supersymmetric quantum mechanics of relativistic and non-relativisitc systems, duality transformations for power–law potentials and conformal transformations. New aspects on the spreading of wave packets are also discussed.
Research & information: general --- Technology: general issues --- non-Hermitian quantum dynamics --- unitary vicinity of exceptional points --- degenerate perturbation theory --- Hilbert-space geometry near EPs --- relativistic wave equation --- Klein–Gordon equation --- Dirac equation --- Proca equation --- supersymmetry --- quantum mechanics --- shape invariance --- curved space --- position-dependent mass --- supersymmetric quantum mechanics --- self-adjoint extensions --- infinite square well --- contact potentials --- power-law duality --- classical and quantum mechanics --- semiclassical quantization --- quark confinement --- spreading wave function --- scattering --- localization --- Klein–Gordon oscillator --- Green’s function --- semiclassical theories and applications --- classical general relativity --- n/a --- Klein-Gordon equation --- Klein-Gordon oscillator --- Green's function
Book
Year: 2021 Publisher: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute
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This book collects contributions to the Special Issue entitled "Symmetries in Quantum Mechanics and Statistical Physics" of the journal Symmetry. These contributions focus on recent advancements in the study of PT–invariance of non-Hermitian Hamiltonians, the supersymmetric quantum mechanics of relativistic and non-relativisitc systems, duality transformations for power–law potentials and conformal transformations. New aspects on the spreading of wave packets are also discussed.
non-Hermitian quantum dynamics --- unitary vicinity of exceptional points --- degenerate perturbation theory --- Hilbert-space geometry near EPs --- relativistic wave equation --- Klein–Gordon equation --- Dirac equation --- Proca equation --- supersymmetry --- quantum mechanics --- shape invariance --- curved space --- position-dependent mass --- supersymmetric quantum mechanics --- self-adjoint extensions --- infinite square well --- contact potentials --- power-law duality --- classical and quantum mechanics --- semiclassical quantization --- quark confinement --- spreading wave function --- scattering --- localization --- Klein–Gordon oscillator --- Green’s function --- semiclassical theories and applications --- classical general relativity --- n/a --- Klein-Gordon equation --- Klein-Gordon oscillator --- Green's function
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