
Review of Short Phrases and Links 
This Review contains major "Wave Equation" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 The wave equation is an important secondorder linear partial differential equation of waves, such as sound waves, light waves and water waves.
 The wave equation is linear in u and it is left unaltered by translations in space and time.
 The wave equation is a fundamental model in mathematical physics that describes how a disturbance travels through matter.
 The wave equation is the prototypical example of a hyperbolic partial differential equation.
 The wave equation is a differential equation that describes the evolution of a harmonic wave over time.
 Wave equation for matter reminiscent of Maxwell's equations for electromagnetic waves.
 QUOTE (ii) psi should be normalized all the way The wave equation, the Klein Gordon equation and the Schrodinger equation would all fail to met that.
 Wave mechanics have been used extensively in piles for many years but the solution of the wave equation has been almost exclusively a numerical one.
 The approach is based on a solution to the homogeneous wave equation for random inhomogeneous media.
 The Klein–Gordon equation was first considered as a quantum wave equation by Schrödinger in his search for an equation describing de Broglie waves.
 Solving the Schrodinger equation is comparible in difficult, computer wise, to solving the classical wave equation.
 The KleinGordon equation was first considered as a quantum wave equation by Schrödinger in his search for an equation describing de Broglie waves.
 One of the first attempts at a relativistic quantum mechanical wave equation was the KleinGordon (KG) equation.
 A general solution for the wave equation in one dimension was given by d'Alembert.
 That's what the Schroedinger wave equation describes: the probability that you will find a quantum there.
 In particular, consider the wave equation in one dimension, for example, as applied to a string.
 A pulse traveling through a string with fixed endpoints as modeled by the wave equation.
 In fact, symmetric equations can be written when all charges are zero, and this is how the wave equation is derived (see immediately above).
 The story I heard is that Schrödinger went to Switzerland with two goals: to keep his mistress happy and to derive a wave equation for matter.
 By refining the wave equation with a gravitational potential, the gravitational force and the mass are derived.
 When the mass is zero this is just the free wave equation.
 A KleinGordon Equation is a relativistic wave equation for a particle which should reduce to a Schrodinger type of equation.
 From the solution of this wave equation one should be able to select those oscillations which were feasible for the motons within the atoms.
 Hyperbolic equations: wave equation, method of characteristics, shocks and weak solutions.
 An unobserved system, according to the Copenhagen interpretation of quantum theory, evolves in a deterministic way determined by a wave equation.
 In physics, the acoustic wave equation governs the propagation of acoustic waves through a material medium.
 To develop the wave equation, Equation 1, from first principles we will consider the disturbance of a fluidlike medium.
 Common examples of linear PDEs include the heat equation, the wave equation and Laplace's equation.
 I gave a lecture at École Polytechnique in April, 2005, on the propagation of singularities for the wave equation on manifolds with corners.
 Atoms and molecules are empirically observed to obey some type of wave equation.
 For the derivation of the wave equation (as well as the other PDEs, such as heat and Poisson's equations), check Appendix 1 of the Folland book above.
 In this article, it is most appropriate to use SI units through the motivation and derivation of the homogeneous wave equation.
 Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.
 In fact, since the propagator is obtained by inverting the wave equation, in general it will have singularities on shell.
 Similar considerations apply to other equations of mathematical physics, notably, the wave equation and Helmholtz equation.
 The examples of the type of phenomena related to each of the main PDEs are The wave equation can be used to model the motion of a plucked guitar string.
 Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.
 Photons are detected as particles, at a particular point, but their motion from source to detector is described by a wave equation.
 In 1932 Ettore Majorana proposed an infinitecomponent relativistic wave equation for particles of arbitrary integer and halfinteger spin.
 The Dirac equation is a relativistic quantum mechanical wave equation invented by Paul Dirac in 1928.
 The relativistic generalisations of this wave equation are the Dirac equation and the KleinGordon equation.
 In quantum mechanics all elementary particles and atoms may be described in terms of a wave equation.
 This is the central assumption of manyworlds: that the wave equation is obeyed universally and at all times.
 Manyworlds is the unavoidable implication of any quantum theory which obeys some type of linear wave equation.
 Maxwell's equations can be written in the form of a wave equation with sources.
 Indeed, the Schrödinger equation can be viewed as a form of the wave equation applied to matter waves.
 I had to show that the form of the electromagnetic wave equation is covariant between stationary frame S and moving frame S' under a Lorentz transformation.
 Introduction The wave equation is the prototypical example of a hyperbolic partial differential equation.
 This is a commonly encountered form of the Schrödinger wave equation, though not the most general one.
 The Electronic Structure of Atoms The electronic structure of atoms can be understood in terms of the Schrödinger wave equation.
 The importance of Dirac's work lies essentially in his famous wave equation, which introduced special relativity into Schrödinger's equation.
 Solutions to the Schrödinger wave equation correspond to modes of electron resonance and are formally called wavefunctions.
 We review the spinor calculus and the construction of generalized Pauli matrices for any spin, and a few properties of the wave equation and its solutions.
 To introduce the problem we first give a brief sketch of the physics in terms of a given mode (solution of the wave equation).
 These formulas provide the solution for the initialvalue problem for the wave equation.
 Derivation and solution of wave equation for plane and spherical waves.
 Solution of a general initialvalue problem The wave equation is linear in u and it is left unaltered by translations in space and time.
 Since the Schrödinger equation is a wave equation and all objects can be considered waves in quantum mechanics, interference is ubiquitous.
 The Fourier transform breaks up a wave into sinusodal components and is useful for analyzing the wave equation.
 In the most general case, any function of x, y, z, and t that is a nontrivial solution to the wave equation is a wave.
 Dirac comes up with a relativistic quantum mechanical wave equation for the electron.
 His relativistic wave equation for the electron was the first successful attack on the problem of relativistic quantum mechanics.
 Everett also assumed that the wavefunction obeyed the same wave equation during observation or measurement as at all other times.
 It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome.
 This is a commonly encountered form of the Schrödinger wave equation, though not the most general one.
 The wavefunction of the Schrödinger wave equation reduces to the three equations that when solved lead to the first three quantum numbers.
 This form of the Schrödinger equation is referred to as the Schrödinger wave equation.
 Dirac realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility of antielectrons.
 The Hamiltonian in the Schrödinger wave equation used in quantum chemistry does not contain terms for the spin of the electron.
 One finds a wave equation and that equation is invariant under boosts where the speed of light is replaced by the speed of sound.
 Important partial differential equations include the heat equation, the wave equation, and Laplace's equation, which are central to mathematical physics.
 Introduction to partial differential equations, including the heat equation, wave equation and Laplace's equation.
Categories
 Maxwell's Equations
 Schr
 Physics > Quantum Theory > Quantum Field Theory > Dirac Equation
 Electromagnetic Waves
 Schrödinger
Related Keywords
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