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searching for Free particle 97 found (142 total)

Hamiltonian (quantum mechanics) (5,042 words) [view diff] exact match in snippet view article

energy eigenstates have the same energy. A simple example of this is a free particle, whose energy eigenstates have wavefunctions that are propagating plane

Moving particle semi-implicit method (1,735 words) [view diff] exact match in snippet view article find links to article

Research, Vol 32, pp. 124-131, 2010. A. Shakibaeinia and Y.C. Jin "A mesh-free particle model for simulation of mobile-bed dam break." Advances in Water Resources

Hamilton's principle (2,268 words) [view diff] exact match in snippet view article find links to article

the use of the action principle via the Euler–Lagrange equations. A free particle (mass m and velocity v) in Euclidean space moves in a straight line

Quantum nondemolition measurement (1,080 words) [view diff] exact match in snippet view article find links to article

free particle can be QND because the momentum distribution is preserved by the particle's self-Hamiltonian p2/2m. Because the Hamiltonian of the free

Interaction picture (2,324 words) [view diff] no match in snippet view article find links to article

solution to the many-body Schrödinger equation as the solution to the free-particle problem plus some unknown interaction parts. Equations that include

Phase-space formulation (3,604 words) [view diff] no match in snippet view article find links to article

The phase-space formulation is a formulation of quantum mechanics that places the position and momentum variables on equal footing in phase space. The

Path integral formulation (14,277 words) [view diff] no match in snippet view article find links to article

to go from point x to point y as an integral over all paths. For a free-particle action (for simplicity let m = 1, ħ = 1) S = ∫ x ˙ 2 2 d t , {\displaystyle

Artin billiard (504 words) [view diff] exact match in snippet view article find links to article

studied by Emil Artin in 1924. It describes the geodesic motion of a free particle on the non-compact Riemann surface H / Γ , {\displaystyle \mathbb {H}

Darwin Lagrangian (2,582 words) [view diff] exact match in snippet view article find links to article

+ L int , {\displaystyle L=L_{\text{f}}+L_{\text{int}},} where the free particle part is L f = 1 2 m 1 v 1 2 + 1 8 c 2 m 1 v 1 4 + 1 2 m 2 v 2 2 + 1

Helmholtz equation (2,976 words) [view diff] exact match in snippet view article find links to article

equation, the diffusion equation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the wave equation for the electric

Light-cone coordinates (1,362 words) [view diff] exact match in snippet view article find links to article

{L}}_{0}.} This result agrees with a result cited in the literature. For a free particle of mass m {\displaystyle m} the action is S = ∫ L d σ , L = − 1 2 [

Born series (742 words) [view diff] exact match in snippet view article find links to article

V , {\displaystyle G_{0}V,} where G 0 {\displaystyle G_{0}} is the free particle Green's operator). It is closely related to Born approximation, which

Relation between Schrödinger's equation and the path integral formulation of quantum mechanics (2,154 words) [view diff] no match in snippet view article find links to article

{H}}t\right)|0\rangle } where we have assumed the initial state is a free-particle spatial state | q 0 ⟩ {\displaystyle \left|q_{0}\right\rangle } .[clarification

Effective mass (solid-state physics) (3,717 words) [view diff] exact match in snippet view article

that is used to simplify band structures by modeling the behavior of a free particle with that mass. For some purposes and some materials, the effective

Virtual displacement (1,741 words) [view diff] no match in snippet view article find links to article

In analytical mechanics, a branch of applied mathematics and physics, a virtual displacement (or infinitesimal variation) δ γ {\displaystyle \delta \gamma

Crystal momentum (1,474 words) [view diff] exact match in snippet view article find links to article

energy of a free particle). In regions where the band is approximately parabolic the crystal momentum is equal to the momentum of a free particle with momentum

Schrödinger group (1,725 words) [view diff] exact match in snippet view article find links to article

The Schrödinger group is the symmetry group of the free particle Schrödinger equation. Mathematically, the group SL(2,R) acts on the Heisenberg group

Belavkin equation (3,349 words) [view diff] exact match in snippet view article find links to article

space. The nonlinear equation describing observation of position of a free particle, which is a special case of the posterior Belavkin equation of the diffusion

W and Z bosons (3,775 words) [view diff] exact match in snippet view article find links to article

of electrons or positrons. Whenever an electron is observed as a new free particle, suddenly moving with kinetic energy, it is inferred to be a result

Newton–Wigner localization (300 words) [view diff] exact match in snippet view article find links to article

{\displaystyle [x_{i}\,,p_{0}]=p_{i}/p_{0}~.} This ensures that the free particle moves at the expected velocity with the given momentum/energy. Apparently

Exciton (4,821 words) [view diff] no match in snippet view article find links to article

transmission and luminescence spectra with the energies below the free-particle band gap of an insulator or a semiconductor. Exciton binding energy

Heat equation (9,803 words) [view diff] no match in snippet view article find links to article

In mathematics and physics, the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph

Hamilton–Jacobi–Einstein equation (1,960 words) [view diff] exact match in snippet view article find links to article

context gij is referred to as the "metric field" or simply "field". For a free particle in curved "empty space" or "free space", i.e. in the absence of matter

Gross–Pitaevskii equation (4,516 words) [view diff] no match in snippet view article find links to article

approximated via a myriad of techniques. The simplest exact solution is the free-particle solution, with V ( r ) = 0 {\displaystyle V(\mathbf {r} )=0} : Ψ ( r

Hadamard's dynamical system (591 words) [view diff] exact match in snippet view article find links to article

trajectories in the Hadamard dynamical system. The motion studied is that of a free particle sliding frictionlessly on the surface, namely, one having the Hamiltonian

Ubykh language (4,612 words) [view diff] exact match in snippet view article find links to article

there is also a free particle corresponding to each: -/ɡʲɨ/ 'and' (free particle /ve/, borrowed from Arabic); -/ɡʲɨlɜ/ 'but' (free particle /ɜʁʷɜ/) Pronominal

Many-body problem (617 words) [view diff] exact match in snippet view article find links to article

can be described with k {\displaystyle k} numbers (take for example a free particle described by its position and velocity vector, resulting in k = 6 {\displaystyle

Thomson scattering (1,537 words) [view diff] exact match in snippet view article find links to article

the classical limit of electromagnetic radiation scattering from a free particle. An incident plane wave accelerates a charged particle which consequently

Classical limit (1,511 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \left\langle V'(X)\right\rangle } do agree. In particular, for a free particle or a quantum harmonic oscillator, the expected position and expected

Wavenumber (1,908 words) [view diff] exact match in snippet view article find links to article

electron wave, in the non-relativistic approximation (in the case of a free particle, that is, the particle has no potential energy): k ≡ 2 π λ = p ℏ = 2

Newtonian limit (532 words) [view diff] exact match in snippet view article find links to article

t'=t\\x'=\gamma (x-v\,t)&\to x'=x-v\,t\end{aligned}}} The geodesic equation for a free particle on curved spacetime with metric g μ ν {\displaystyle g^{\mu \nu }} can

Chemisorption (1,174 words) [view diff] exact match in snippet view article find links to article

and pressure, the change in free energy should be negative. Since a free particle is restrained to a surface, and unless the surface atom is highly mobile

Pauli equation (2,327 words) [view diff] exact match in snippet view article find links to article

force for details of this classical case. The kinetic energy term for a free particle in the absence of an electromagnetic field is just p 2 2 m {\displaystyle

Stochastic electrodynamics (1,417 words) [view diff] exact match in snippet view article find links to article

doi:10.1103/PhysRevA.7.1832. Boyer, T. H. (1973). "Diamagnetism of a free particle in classical electron theory with classical electromagnetic zero-point

Merei-Tiale language (2,214 words) [view diff] exact match in snippet view article find links to article

used in concurrence with the free pronoun and is often followed by the free particle nga 'only' as seen in example 5 and 6 below. (5) I ART.PN nau 1SG nese-gu

Spacetime diagram (6,178 words) [view diff] exact match in snippet view article find links to article

inertial reference frame a free particle has a straight world line. In a non-inertial reference frame the world line of a free particle is curved. Take the example

Ludwig Lange (physicist) (392 words) [view diff] exact match in snippet view article

inertia then states that relative to any inertial system, any fourth free particle will move uniformly. Lange, L. (1885). "Über die wissenschaftliche Fassung

Quantum configuration space (444 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {R} ^{3}} is the classical configuration space of free particle which has finite degrees of freedom, and d 3 x {\displaystyle d^{3}x}

Compton wavelength (1,627 words) [view diff] exact match in snippet view article find links to article

wavelength appears in the relativistic Klein–Gordon equation for a free particle: ∇ 2 ψ − 1 c 2 ∂ 2 ∂ t 2 ψ = ( m c ℏ ) 2 ψ . {\displaystyle \mathbf

Expansion of the universe (4,556 words) [view diff] case mismatch in snippet view article find links to article

ISSN 2214-4048. Whiting, Alan B. (2004). "The Expansion of Space: Free Particle Motion and the Cosmological Redshift". The Observatory. 124: 174.

Propagator (6,183 words) [view diff] exact match in snippet view article find links to article

{\displaystyle K(x,t;x',t')=K(x,x';t-t').} The propagator of a one-dimensional free particle, obtainable from, e.g., the path integral, is then K ( x , x ′ ; t )

Ponderomotive energy (584 words) [view diff] exact match in snippet view article find links to article

} The formula for the ponderomotive energy can be easily derived. A free particle of charge q {\displaystyle q} interacts with an electric field E cos

Degenerate matter (3,072 words) [view diff] exact match in snippet view article find links to article

white dwarf, where most of the electrons would be treated as occupying free particle momentum states. Exotic examples of degenerate matter include neutron

Hadronization (1,535 words) [view diff] exact match in snippet view article find links to article

decays before it can hadronize. The top quark is therefore almost a free particle. Rafelski, Johann (2015). "Melting hadrons, boiling quarks". The European

Multibody system (1,818 words) [view diff] exact match in snippet view article find links to article

simplest bodies or elements of a multibody system were treated by Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies

Nakanai language (2,748 words) [view diff] exact match in snippet view article find links to article

appears post-verbally in first nominal slot." Goals are encoded by the free particle te. It is the case of the entity toward which the action is directed

Momentum operator (2,144 words) [view diff] exact match in snippet view article find links to article

using the plane wave solution to Schrödinger's equation of a single free particle, ψ ( x , t ) = e i ℏ ( p x − E t ) , {\displaystyle \psi (x,t)=e^{{\frac

Scattering length (1,103 words) [view diff] exact match in snippet view article find links to article

{\displaystyle l=0} ) outside of the well is just the same as for a free particle: − ℏ 2 2 m u ″ ( r ) = E u ( r ) , {\displaystyle -{\frac {\hbar

History of classical mechanics (2,844 words) [view diff] exact match in snippet view article find links to article

Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature,

Mathematical formulation of the Standard Model (7,734 words) [view diff] exact match in snippet view article find links to article

state vector should only change when particles interact, meaning a free particle is one whose quantum state is constant. This corresponds to the interaction

Objective-collapse theory (3,212 words) [view diff] exact match in snippet view article find links to article

S2CID 16123332. Bassi, Angelo (2005). "Collapse models: analysis of the free particle dynamics". Journal of Physics A: Mathematical and General. 38 (14):

Feynman checkerboard (1,493 words) [view diff] case mismatch in snippet view article find links to article

1216/rmj-1974-4-3-497. ISSN 0035-7596. Ord, G.N. (1996). "The Schrödinger and Dirac Free Particle Equations without Quantum Mechanics". Annals of Physics. 250 (1). Elsevier

Nephrocalcinosis (1,582 words) [view diff] exact match in snippet view article find links to article

is another theory of how the disease manifests. This is called the free particle theory. This theory says that the increasing concentration of lithogenic

Geodesics as Hamiltonian flows (1,113 words) [view diff] exact match in snippet view article find links to article

correctly, one must use the inverse of the metric. The motion of a free particle on a curved surface still has exactly the same form as above, i.e. consisting

Attractor (3,885 words) [view diff] exact match in snippet view article find links to article

units of time. For example, if the system describes the evolution of a free particle in one dimension then the phase space is the plane R 2 {\displaystyle

Hilbert–Pólya conjecture (1,679 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \varphi _{n}^{0}} are the eigenvalues and eigenstates of the free particle Hamiltonian. This equation can be taken to be a Fredholm integral equation

Four-momentum (3,739 words) [view diff] exact match in snippet view article find links to article

{1-{\frac {v^{2}}{c^{2}}}}},} where L is the relativistic Lagrangian for a free particle. From this, glossing over these details, The variation of the action

Pontecorvo–Maki–Nakagawa–Sakata matrix (2,071 words) [view diff] no match in snippet view article find links to article

⁠ ν 3 {\displaystyle \nu _{3}} ⁠, which diagonalize the neutrino's free-particle Hamiltonian. Observations of neutrino oscillation established experimentally

Photoelectric effect (7,026 words) [view diff] exact match in snippet view article find links to article

binding, and the rest contributes to the electron's kinetic energy as a free particle. Because electrons in a material occupy many different quantum states

Lippmann–Schwinger equation (2,565 words) [view diff] exact match in snippet view article find links to article

i\epsilon }}V|\psi ^{(\pm )}\rangle .} By insertion of a complete set of free particle states, | ψ ( ± ) ⟩ = | ϕ ⟩ + ∫ d β | ϕ β ⟩ E − E β ± i ϵ ⟨ ϕ β | V

List of things named after Erwin Schrödinger (308 words) [view diff] exact match in snippet view article find links to article

Schrödinger functional Schrödinger group, the symmetry group of the free particle Schrödinger equation Schrödinger (crater), a lunar impact crater Vallis

Integrable system (3,407 words) [view diff] exact match in snippet view article find links to article

structure. To explain quantum integrability, it is helpful to consider the free particle setting. Here all dynamics are one-body reducible. A quantum system

Chaos theory (13,052 words) [view diff] exact match in snippet view article find links to article

Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature,

Laplace–Runge–Lenz vector (10,215 words) [view diff] exact match in snippet view article find links to article

quantum mechanical bound Kepler problem is equivalent to the problem of a free particle confined to a three-dimensional unit sphere in four-dimensional space

Sterile neutrino (4,597 words) [view diff] exact match in snippet view article find links to article

is massless, chirality is not conserved during the propagation of a free particle through space (nominally, through interaction with the Higgs field)

Scalar field theory (4,903 words) [view diff] exact match in snippet view article find links to article

ultraviolet cutoff is removed. Consequently, the propagator becomes that of a free particle and the field is no longer interacting. For a φ4 interaction, Michael

Uncertainty principle (19,263 words) [view diff] exact match in snippet view article find links to article

in dynamic variables, like the hands of a clock or the motion of a free particle; observable time concerns time as an observable, the measurement of

Continuous spontaneous localization model (4,916 words) [view diff] exact match in snippet view article find links to article

predictions of quantum mechanics, where no radiation is expected from a free particle. The predicted CSL-induced emission rate at frequency ω {\displaystyle

Källén–Lehmann spectral representation (878 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \Delta (p;\mu ^{2})={\frac {1}{p^{2}-\mu ^{2}+i\epsilon }}} a free particle propagator. Now, as we have the exact propagator given by the time-ordered

Lagrangian mechanics (14,711 words) [view diff] exact match in snippet view article find links to article

flat 3D real space the geodesics are simply straight lines. So for a free particle, Newton's second law coincides with the geodesic equation and states

Self-adjoint operator (8,156 words) [view diff] no match in snippet view article find links to article

half-line. Nevertheless, the Hamiltonian p 2 {\displaystyle p^{2}} of a "free" particle on a half-line has several self-adjoint extensions corresponding to

Hamilton–Jacobi equation (8,209 words) [view diff] exact match in snippet view article find links to article

in the next sections. In spherical coordinates the Hamiltonian of a free particle moving in a conservative potential U can be written H = 1 2 m [ p r

Ghirardi–Rimini–Weber theory (3,182 words) [view diff] exact match in snippet view article find links to article

S2CID 44038399. Bassi, Angelo (2005-04-08). "Collapse models: analysis of the free particle dynamics". Journal of Physics A: Mathematical and General. 38 (14):

Bessel function (12,228 words) [view diff] exact match in snippet view article find links to article

Schrödinger equation (in spherical and cylindrical coordinates) for a free particle Position space representation of the Feynman propagator in quantum field

Langevin equation (5,246 words) [view diff] exact match in snippet view article find links to article

particular, the late time behavior depicts thermal equilibrium. Consider a free particle of mass m {\displaystyle m} with equation of motion described by m d

Thermodynamic temperature (13,823 words) [view diff] exact match in snippet view article find links to article

underlying thermodynamic temperature: the kinetic energy of atomic free particle motion. The revision fixed the Boltzmann constant at exactly 1.380649×10−23 joules

Quantum walk (2,600 words) [view diff] exact match in snippet view article find links to article

{R} _{\geq 0}\to \mathbb {C} } which satisfies the one-dimensional, free particle Schrödinger equation i ℏ ∂ ψ ∂ t = − ℏ 2 2 m ∂ 2 ψ ∂ x 2 {\displaystyle

Green's function (many-body theory) (4,547 words) [view diff] exact match in snippet view article

two-point ( n = 1 {\displaystyle n=1} ) thermal Green function for a free particle is G ( k , ω n ) = 1 − i ω n + ξ k , {\displaystyle {\mathcal {G}}(\mathbf

Gas in a box (2,746 words) [view diff] exact match in snippet view article find links to article

P_{E}~dE=P_{p}{\frac {dp}{dE}}~dE} For a particle in a box (and for a free particle as well), the relationship between energy E {\displaystyle E} and momentum

Resonant high harmonic generation from laser ablated plasma plumes (1,103 words) [view diff] exact match in snippet view article find links to article

harmonics. In Corkum's three-step model, the electron is treated as a free particle having no effect of the coulomb potential. Since the tunnel ionization

Zero-point energy (26,811 words) [view diff] exact match in snippet view article find links to article

just shown. A similar result is easily worked out for the case of a free particle instead of a dipole oscillator. What we have here is an example of a

Depletion force (4,793 words) [view diff] exact match in snippet view article find links to article

dispersion particles resists the depletion force between them, pulling the free particle away from the adhered particle. A force balance of the particles at

Ingrian grammar (4,922 words) [view diff] exact match in snippet view article find links to article

inherited from Proto-Finnic, while others are borrowed from Russian. The free particle i has the same function as the clitic -ki, and both can be used together

Airy beam (2,417 words) [view diff] no match in snippet view article find links to article

beam is the only exactly shape-preserving accelerating solution to the free-particle Schrödinger equation (or 2D paraxial wave equation). However, in two

Smoothed-particle hydrodynamics (9,785 words) [view diff] exact match in snippet view article find links to article

J. Quinlan; M. Basa; M. Lastiwka (2006). "Truncation error in mesh-free particle methods" (PDF). International Journal for Numerical Methods in Engineering

Health and safety hazards of nanomaterials (5,392 words) [view diff] exact match in snippet view article find links to article

of dry sweeping with a broom, avoiding handling nanomaterials in a free particle state, storing nanomaterials in containers with tightly closed lids

Electron scattering (5,071 words) [view diff] exact match in snippet view article find links to article

to electric fields. Rewriting this as the equation of motion for a free particle of charge q mass m, this becomes: m d v d t = q E + q v × B {\displaystyle

Molecular Hamiltonian (5,204 words) [view diff] exact match in snippet view article find links to article

sum Mtot of the masses of all the particles. In quantum mechanics a free particle has as state function a plane wave function, which is a non-square-integrable

Representation theory of the Lorentz group (19,748 words) [view diff] exact match in snippet view article find links to article

Lorentz group. See Dalitz & Peierls 1986 See formula (1) in S-matrix#From free particle states for how free multi-particle states transform. Weinberg 2002,

Laplacian of the indicator (4,274 words) [view diff] exact match in snippet view article find links to article

Carreau, M.; Farhi, E.; Gutmann, S. (1990), "Functional integral for a free particle in a box", Physical Review D, 42 (4): 1194–1202, Bibcode:1990PhRvD.

Spectrum (physical sciences) (2,734 words) [view diff] exact match in snippet view article

electrons in a metal. In particular, the position and momentum of a free particle has a continuous spectrum, but when the particle is confined to a limited

Quantum LC circuit (6,688 words) [view diff] exact match in snippet view article find links to article

one for the "CM" coordinate that is the differential equation of a free particle, and the other for the charge difference coordinate, which is the Schrödinger

Static forces and virtual-particle exchange (8,459 words) [view diff] exact match in snippet view article find links to article

functions of spacetime. The first term in the argument represents the free particle and the second term represents the disturbance to the field from an

Transition metal dichalcogenide monolayers (10,542 words) [view diff] exact match in snippet view article find links to article

picture the binding energy EB is defined as the difference between the free particle band gap and the optical band gap and represent, as usual, the energy

Non-topological soliton (6,328 words) [view diff] exact match in snippet view article find links to article

shows that the NTS solution is energetically favored over a plane wave (free particle) only if g > 2.3 {\displaystyle g>2.3} for even very small m H {\displaystyle

Bibliography of Max Born (8,976 words) [view diff] exact match in snippet view article find links to article

des kräftefreien Teilchens" [On the quantum mechanics of the force-free particle]. Z. Phys. 150 (1): 106–117. Bibcode:1958ZPhy..150..106B. doi:10.1007/bf01338519

Coulomb scattering (9,863 words) [view diff] exact match in snippet view article find links to article

infinite and the asymptotic radial wavefunction never approaches the free particle wavefunction. These mathematical issues can be solved by applying parabolic