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Topic: Relativistic wave equations

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	Relativistic wave equations - Wikipedia, the free encyclopedia
		The first such equation was discovered by Erwin Schrödinger himself; however, he realized that this equation, now called the Klein-Gordon equation, gave incorrect results when used to calculate the energy levels of hydrogen.
		Schrödinger discarded his relativistic wave equation, only to realize a few months later that its nonrelativistic limit (what is now called the Schrödinger equation) was still of importance.
		All the particle equations except the Breit, the Yang-Mills and Yang-Mills-Higgs are non-linear.
	en.wikipedia.org /wiki/Relativistic_wave_equations (230 words)

	Relativistic particle - Wikipedia, the free encyclopedia
		A relativistic particle is a particle moving with a speed close to the speed of light, such that effects of special relativity are important for the description of its behavior.
		(This condition implies that their speed is close to the speed of light.) Such relativistic particles are generated in particle accelerators, and are naturally occurring in cosmic radiation.
		In astrophysics, jets of relativistic plasma are produced by the centers of active galaxies and quasars.
	en.wikipedia.org /wiki/Relativistic (167 words)

	TIQM: 3.3 The Transactional Model and Relativistic Quantum Mechanics
		Another problem which raises some concern about the statistical interpretation of quantum mechanics in the relativistic domain is the observation that the solutions of the field equations cannot always be used to construct a relativistically invariant or positive definite probability density (Bjorken, 1964).
		Thus, while differential field equations and their solutions remain an indispensible feature of relativistic quantum field theory (Bjorken, 1965), the problem of the identity of these solutions (see Section 2.1) is made more severe because the statistical interpretation, at least in its simplest form, has proved inadequate.
		The relativistic wave equations which do have advanced as well as retarded solutions have been treated with suspicion because they do not uniquely describe the state of a given system {footnote 18}.
	mist.npl.washington.edu /npl/int_rep/tiqm/TI_33.html (3611 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		A wave function that solves the Weyl equation must then be a two-component column vector (since the operator equation involves 2 by 2 matrices).
		We reviewed why solutions to Weyl's equations must also solve the Klein-Gordon equation, and used the Klein-Gordon equation to isolate and solve for their space-time dependence, getting (for a particle with momentum \vec{k}) that each spin component was some constant times the wave equation solution for momentum \vec{k}.
		The alternate choice for linearizing the relativistic dispersion relation --- choosing \alpha = - \sigma --- gives, by the same analysis, solutions which must be in a spin down eigenstate of the spin component along the direction of their motion.
	www.emory.edu /PHYSICS/Faculty/Benson/380-96/notes/25.txt (429 words)

	Amazon.ca: Relativistic Quantum Mechanics. Wave Equations: Books: D.A. Bromley,Walter Greiner (Site not responding. Last check: 2007-11-01)
		Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles.
		Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner).
		A revised and up-to-date text concentrating on the wave equations for spin-0 and spin-1/2 particles.
	www.amazon.ca /Relativistic-Quantum-Mechanics-Wave-Equations/dp/3540674578 (418 words)

	Baylor University \|\| Department of Physics \|\| Courses (Site not responding. Last check: 2007-11-01)
		Magnetohydrodynamics and plasma physics, advanced relativistic electrodynamics,collisions of charged particles, scattering, Lienard-Wiechert potentials and radiation by moving charges, Bremsstrahlung, the method of virtual quanta, dynamic multipole fields, radiation damping, self-fields of a particle, and scattering and absorption by a bound system.
		Schrodinger equation, eigenfunctions and eigenvalues, harmonic oscillator, and hydrogen atom.
		Relativistic astrophysics, and the final stages of stellar evolution; supernovae, binary stars, accretion disks, pulsars; extragalactic radio sources; active galactic nuclei; compact objects.
	www.baylor.edu /physics/index.php?id=11336 (800 words)

	Wave Equations
		The purpose of this section is to give a plausible derivation of such an equation by examining how the Maxwell wave equation works for a single-particle (photon) wave, and constructing parallel equations for particles which, unlike photons, have nonzero rest mass.
		The wave equation operator applied to the plane wave describing the particle propagation yields the energy-momentum relationship for the particle.
		The effect of a potential on a de Broglie wave was considered by Sommerfeld in an attempt to generalize the rather restrictive conditions in Bohr's model of the atom.
	galileo.phys.virginia.edu /classes/252/wave_equations.html (1267 words)

	Friedrich-Schiller-Universität Jena - 2.2. Main Study Course (Diploma in Physics)
		Kinetic theory of gases: Boltzmann equation; H theorem; transport coefficients; Euler equation and Navier- Stokes equation.
		Introduction: relativistic wave mechanics, Lagrangian and Hamiltonian formulations, symmetries.
		Relativistic Astrophysics (Lecture 2 h and Seminar 1 h)
	www.uni-jena.de /2_2__Physics_Main.html (4374 words)

	UIC Graduate College -- Courses: Physics (Phys) (Site not responding. Last check: 2007-11-01)
		Wave particle duality; wave functions; Schroedinger equation; mathematical structure of quantum mechanics; operators and observables; matrix representation of operators; three-dimensional Schroedinger equation.
		Prerequisites: Phys 411 and 461; or consent of the instructor.
		Principle of equivalence, the metric field and geodesics, tensor analysis and differential geometry, Einstein's equations and the action principle, gravitational fields and waves, fl holes.
	www.uic.edu /depts/grad/courses/phys.shtml (1114 words)

	5. Advanced Waves and the Appropriateness of Wave Equations
		We must bear in mind, however, that the Schrödinger equation is ultimately not physically correct because it is not relativistically invariant.
		When a suitable relativistic wave equations is reduced to the Schrödinger equation by taking a non-relativistic limit[5], the reduction procedure leads to two distinct equations, the Schrödinger equation and another equation of the form:
		Equations (1) and (2) are equally valid non-relativistic reductions of relativistic dynamics, but equation (2) is usually dropped because it has negative energy eigenvalues.
	mist.npl.washington.edu /npl/int_rep/ti_over/node5.html (576 words)

	Physics Honours Program
		Boltzmann transport equation, approximate solutions; the H theorem and the problem of irreversibility; Liouville equation, time correlation functions, Linear response theory; Brownian motion; Boltzmann's ergodic hypothesis, Gibbs mixing, Birkoff's theorem, the baker's map.
		Relativistic notation and 4-vectors, vector potential, action of a particle in an EM field and action of an EM field, Gauge invariance, tensor of EM field.
		Spin waves; low temperature thermodynamics of magnetic systems; systems with RKKY interactions; mean field theory of itinerant electron magnetism; incommensurability; frustration and spin glasses.
	www.phys.unsw.edu.au /COURSES/HONOURS/honourslecture.html (768 words)

	University of Calgary: Calendar: Courses: Physics
		M9 Waves I. Equations for travelling and standing waves; waves in gases, fluids, solids, and on strings; acoustic waves; superposition; wave speed; intensity and intensity level; Doppler shift for sound waves; energy transfer by radiation.
		Wave equation and its harmonic solutions; waves in gases, fluids, solids, and on strings; acoustic waves; superposition; group and phase velocity; energy transport by waves; reflection and transmission; complex impedance; normal modes.
		Relativistic kinematics; spacetime diagrams; relativistic energy and momentum conservation with applications to particle physics.
	www.ucalgary.ca /pubs/calendar/2005/what/courses/PHYS.htm (2107 words)

	Course Descriptions - 78 Physics - Rensselaer Catalog 97\|98 (Site not responding. Last check: 2007-11-01)
		Mechanics with emphasis on equilibrium and statics, fluids, oscillations, and waves.
		Linear differential equations for classical systems; complex analysis; Fourier Transforms for waves; wave equations and solutions; vector analysis for classical fields; Lorentz transformation and four vectors.
		Maxwell's equations and wave propagation with applications to optics.
	www.rpi.edu /dept/catalog/97-98/Courses/78.html (1142 words)

	Science-Shop > Superluminal Wave Motion
		A major aim of this book is to elucidate what is really meant and implied by superluminal wave motion a question that has caused much confusion until now.
		They also clarify the meaning of several types of superluminal velocity that appear in quantum theory; for example, the Hegerfeldt paradox and formalism is given in sufficient detail that students will also be able to follow the arguments.
		It is proved that all linear relativistic wave equations of mathematical physics (Maxwell, Dirac, Weyl, the homogeneous wave equation and the Klein-Gordon equation) possess arbitrary velocities solutions, which are undistorted progressive waves.
	www.wissenschaft-online.de /blatt/d_shop_buch&_knv_dok_nr=052980211 (155 words)

	RPI Physics, Applied Physics, & Astronomy: Course Descriptions: Undergraduate Physics
		Vector calculus and partial differential equations, especially with applications to electrodynamics.
		Propagation of electromagnetic waves in inhomogeneous media and scattering phenomena.
		Relativistic electrodynamics and fields associated with accelerated charged particles.
	www.rpi.edu /AFS/dept/phys/undergraduate/courses/gradphys.html (624 words)

	Departments and Programs -- Ch5: 2000-2001 UVa Graduate Record (Site not responding. Last check: 2007-11-01)
		Includes the principle of equivalence; effects of gravitation on other systems and fields; general tensor analysis in curved spaces and gravitational field equations; Mach's principle, tests of gravitational theories: perihelion precession, red shift, bending of light, gyroscopic precession, radar echo delay; gravitational radiation; relativistic stellar structure and cosmography; and a short survey of cosmological models.
		Development of the theory of special relativity, relativistic electrodynamics, radiation from moving charges, classical electron theory, and Lagrangian and Hamiltonian formulations of electrodynamics.
		Discusses the theory of scattering and relativistic wave equations.
	www.virginia.edu /registrar/records/00gradrec/chapter5/gchap5-7.34.html (1217 words)

	Amazon.com: Relativistic Quantum Mechanics: Wave Equations (Theoretical Physics): Books: Walter Greiner (Site not responding. Last check: 2007-11-01)
		The description of phenomena at high energies requires the investigation of relativistic wave equations.
		positron wave function, pionic atom, lower continuum, positron states, velocity operator, muonic atoms, helicity operator, hole theory, negative energy solutions, parity transformation, energy continuum, nonrelativistic limit, relativistic wave equation, charge conjugation, spatial reflection, spinor components, space inversion, optical potential, energy eigenvalues, nonrelativistic theory, negative energy states, negative helicity, conformal group, spatial rotations, time inversion
		This book fights that trend by covering in detail the topics that are thrown by the wayside in the traditional coverage, spending (investing?) page after page on topics that barely merit an exercise or a footnote in more traditional treatements.
	www.amazon.com /Relativistic-Quantum-Mechanics-Equations-Theoretical/dp/038757266X (1215 words)

	UNITARY REPRESENTATIONS OF THE POINCARÉ GROUP AND RELATIVISTIC WAVE EQUATIONS
		Complete knowledge of every free particle states and their behaviour can be obtained once all the unitary irreducible representations of the Poincaré group are found.
		It is a surprising fact that a simple framework such as the Poincaré group, when unified with quantum theory, fixes our possible picture of particles severely and without exception.
		In this connection, the theory of unitary representations of the Poincaré group provides a fundamental concept of relativistic quantum mechanics and field theory.
	www.worldscibooks.com /physics/0537.html (210 words)

	Optics Courses (Site not responding. Last check: 2007-11-01)
		Topics include relativistic particle dynamics; radiation by moving charges; multipole fields; radiation damping and self- fields of a particle; collisions between charged particles and energy loss; radiative processes; and classical field theory.
		Includes basic phenomena of ionized gases, static and dynamic shielding, linear waves, instabilities, particles in fields, collisional phenomena, fluid equations, collisionless Boltzman equations, Landau damping, scattering and absorption of radiation in plasmas, elementary nonlinear processes, WKB wave theory, controlled thermonuclear fusion concepts, astrophysical applications, and experimental plasma physics (laboratory).
		Topics vary yearly but include nonlinear effects such as wave coupling, quasilinear relaxation, particle trapping, nonlinear Landau damping, collisionless shocks, solutions; nonneutral plasmas; kinetic theory of waves in a magnetized plasma; anisotropy; inhomogeneity; radiation—ponderomotive force, parametric instabilities, stimulated scattering; plasma optics; kinetic theory, and fluctuation phenomena.
	www.ruf.rice.edu /~dn4550/aboutme/uccourses.html (893 words)

	School of Physics: People : Professors : Helmut Biritzf
		Then it was natural to assume that only the most simple types of fields should be used for their theoretical description.
		Today experiment indicates an underlying multiplet structure of fundamental particles, and we are almost invariably led to wave functions that describe a whole spectrum of particles.
		There is a large class of "regular" wave equations and fields that describe a whole spectrum of particles and which is free of all the difficulties usually associated with higher spin fields.
	www.physics.gatech.edu /people/faculty/hbiritz.html (438 words)

	Klein-Gordon and Schrödinger Equations
		The idea that waves are associated with differential equations was well-established when Debye suggested to Schrödinger that he try to find the appropriate equation for deBroglie waves.
		Although it is impossible to derive Schrödinger's equation, it is possible to make plausible assumptions and then compare the results with experiment.
		However, this equation was first published by Klein and Gordon and is now known as the Klein-Gordon (KG) equation.
	webphysics.davidson.edu /Faculty/wc/WaveHTML/node9.html (192 words)

	Andreas Brandhuber
		Relativistic wave equations for particles of various spins are derived and studied, and the physical interpretation of their solutions are analyzed.
		Finally, basic concepts of Quantum Field Theory, which resolve certain puzzles encountered in the study of Relativistic Quantum Mechanics, are introduced.
		to write down the Lagrangian of a free relativistic scalar particle and to derive the equations of motion and the energy momentum tensor; to quantize the Klein-Gordon field using creation and annihilation operators.
	www.strings.ph.qmul.ac.uk /~andreas/RQM/rqm.html (741 words)

	An Introduction to Relativistic Quantum Field Theory
		In a relatively simple presentation that remains close to familiar concepts, this text for upper-level undergraduates and graduate students introduces the modern developments of quantum field theory.
		Starting with a review of the one-particle relativistic wave equations, it proceeds to a second-quantized description of a system of n particles, examines the restriction that symmetries impose on Lagrangians, and analyzes simple models of field theories.
		Additional topics include the Feynman-Dyson perturbation treatment of relativistic field theories, the formulation of field theory in the Heisenberg picture, the axiomatic formulation of field theory, and dispersion theoretic methods.
	store.doverpublications.com /0486442284.html (255 words)

	[No title]
		Dirac discovered a wave equation that is not only consistent with relativity but also explains particle spin, predicts the existence of antiparticles, and provides us with a deep insight into such symmetries of nature as spatial inversion (parity), charge conjugation and time reversal.
		After Maxwell's great unification of electricity and magnetism in the nineteenth century, no further unification was achieved until Weinberg and Salam devised their standard model in the 1970's - a theory that unifies the weak force and electromagnetism.
		calculate the effects on a Dirac wave function of spatial inversion, charge conjugation and time reversal, and explain how these concepts are used in the modern (Feynman) description of antiparticles
	newton.ex.ac.uk /handbook/00-01/modules/PHY4404.html (626 words)

	USC: Academic Bulletins
		Prior to admission to this department, entering graduate students are expected to have passed with a grade of C or better the following courses or their equivalent: modern physics, mechanics, electromagnetic theory, kinetic theory and statistical mechanics, nuclear physics, and solid state physics.
		Mathematics through advanced calculus, including ordinary and particle differential equations and vector analysis, should also have been completed in the undergraduate program.
		Maxwell's equations applied to problems in electromagnetism and radiation.
	www.sc.edu /bulletin/grad/GPhysics.html (1789 words)

	Yale Physics: Graduate Courses (Site not responding. Last check: 2007-11-01)
		An overview of particle physics including a historical introduction to the standard model, experimental techniques, symmetries, conservation laws, the quark-parton model, and a semiformal treatment of the standard model.
		Basic concepts of differential geometry (manifolds, metrics, connections, geodesics, curvature); Einstein's equations and their application to cosmology, gravitational waves, fl holes, etc.
		Covariant formulation of electrodynamics as an example of a classical relativistic field theory.
	www.yale.edu /physics/graduate/courses.html (797 words)

	Course information
		Relativistic wave equations (Ryder Ch 2, G and R Ch 4.1, 6.2).
		Scalar Quantum Electrodynamics Maxwell equations; Lagrangian formulation of Electromagnetic field equations; Canonical quantisation of EM field in Lorentz gauge; Gauge symmetry; Feynman rules for SQED; photon polarisation sums in scattering probabilities.
		Quantum Mechanics (Schrödinger equations, free particle solution, harmonic oscillator).
	www.pact.cpes.sussex.ac.uk /~markh/Teaching/RQF1/node1.html (509 words)

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