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  2. Velocity potential - Wikipedia

    en.wikipedia.org/wiki/Velocity_potential

    ϕ is known as a velocity potential for u. A velocity potential is not unique. If ϕ is a velocity potential, then ϕ + f(t) is also a velocity potential for u, where f(t) is a scalar function of time and can be constant. Velocity potentials are unique up to a constant, or a function solely of the temporal variable.

  3. Gauge fixing - Wikipedia

    en.wikipedia.org/wiki/Gauge_fixing

    A particular choice of the scalar and vector potentials is a gauge (more precisely, gauge potential) and a scalar function ψ used to change the gauge is called a gauge function. [citation needed] The existence of arbitrary numbers of gauge functions ψ(r, t) corresponds to the U(1) gauge freedom of this theory. Gauge fixing can be done in many ...

  4. Liénard–Wiechert potential - Wikipedia

    en.wikipedia.org/wiki/Liénard–Wiechert_potential

    The Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations , these describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in ...

  5. Lorenz gauge condition - Wikipedia

    en.wikipedia.org/wiki/Lorenz_gauge_condition

    Note added on 26 November 2024: It should be pointed out that Lorenz actually derived the 'condition' from postulated integral expressions for the potentials (nowadays known as retarded potentials), whereas Lorentz (and before him Emil Wiechert) imposed it on the potentials to fix the gauge (see, e.g, his 1904 Encyclopedia article on electron ...

  6. Retarded potential - Wikipedia

    en.wikipedia.org/wiki/Retarded_potential

    Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator. [2]

  7. Landau levels - Wikipedia

    en.wikipedia.org/wiki/Landau_levels

    There is some gauge freedom in the choice of vector potential for a given magnetic field. The Hamiltonian is gauge invariant, which means that adding the gradient of a scalar field to A changes the overall phase of the wave function by an amount corresponding to the scalar field. But physical properties are not influenced by the specific choice ...

  8. Electric potential - Wikipedia

    en.wikipedia.org/wiki/Electric_potential

    Note that, in contrast to the magnitude of an electric field due to a point charge, the electric potential scales respective to the reciprocal of the radius, rather than the radius squared. The electric potential at any location, r , in a system of point charges is equal to the sum of the individual electric potentials due to every point charge ...

  9. Potential flow - Wikipedia

    en.wikipedia.org/wiki/Potential_flow

    Potential flow describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field , which is a valid approximation for several applications.