electromagnetism, a branch of fundamental physics, the matrix representations of the Maxwell's equations are a formulation of Maxwell's equations using matrices,...

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form...

curl of the fourth Maxwell's equation (4) results in a similar differential equation for a magnetic field solving the homogeneous Maxwell's equations: ∇...

functions" in the context of RQM, and "fields" in the context of QFT. The equations themselves are called "wave equations" or "field equations", because they have...

reflection of a layer structure is the sum of an infinite number of reflections. The transfer-matrix method is based on the fact that, according to Maxwell's equations...

consolidate Maxwell's equations using E + i   M {\displaystyle {\mathfrak {E}}+i\ {\mathfrak {M}}} . The real and imaginary components of the equation curl ⁡...

generalization of this equation requires that space and time derivatives must enter symmetrically as they do in the Maxwell equations that govern the behavior of light...

(free field equations, i.e. without interaction terms) of the Klein–Gordon equation, the Dirac equation, the Maxwell equations, the Proca equation, the Rarita–Schwinger...

time for each electric and magnetic vector field component in Maxwell's curl equations. The descriptor "Finite-difference time-domain" and its corresponding...

using vectors, such as kinematics in space and Maxwell's equations, were described entirely in terms of quaternions. There was even a professional research...

method (EBCM). In the method, matrix elements are obtained by matching boundary conditions for solutions of Maxwell equations. It has been greatly extended...

two of Maxwell's equations (the inhomogeneous equations) are the ones that describe the dynamics in the potential formulation. Maxwell's equations (potential...

methods of transforming equations to isolate variables. Linear algebra is a closely related field that investigates linear equations and combinations of them...

Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

discussing the physics implied by these equations since 1887. Early in 1889, Oliver Heaviside had shown from Maxwell's equations that the electric field surrounding...

array of points and enforces Maxwell’s equations at each point. FDFD puts this large set of equations into a matrix and solves all the equations simultaneously...

L=e^{W/2}.} In the matrix representation, the Lorentz rotor is seen to form an instance of the SL(2, C) group (special linear group of degree 2 over the...

relativistic wave equations were found. All these wave equations are of enduring importance. The Schrödinger equation and the Pauli equation are under many...

introduction of translations in the Poincaré group again preserves angles. A larger group of conformal maps for relating solutions of Maxwell's equations was identified...

states. It is possible to write a Dirac-like matrix representation of Maxwell's equations. In such a matrix form the Foldy–Wouthuysen can be applied. There...

density is the quantity ∂D/∂t appearing in Maxwell's equations that is defined in terms of the rate of change of D, the electric displacement field. Displacement...

Hamilton–Jacobi equation Hamilton–Jacobi–Einstein equation Lagrangian mechanics Maxwell's equations Hamiltonian (quantum mechanics) Quantum Hamilton's equations Quantum...

Maxwell's equations, a set of differential equations which directly relate E and B to ρ and J. Alternatively, one can describe the system in terms of...

matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra...

differential equations by expressing AC currents and voltages as exponential functions with imaginary exponents (see § Validity of complex representation). Wietlisbach...

greatest honour in mathematics. The idea of gauge symmetries was introduced in Maxwell's theory. Maxwell's equations are ∇ ⋅ E → = ρ ϵ 0 ∇ × B → − ϵ 0 μ 0...

theories, generalised the classical work of James Maxwell on Maxwell's equations, which had been phrased in the language of a U ⁡ ( 1 ) {\displaystyle \operatorname...

approximately constant. The telegrapher's equations (or just telegraph equations) are a pair of linear differential equations which describe the voltage ( V {\displaystyle...

example is Maxwell's equations, derived to model the elementary electrical and magnetic phenomena known in the mid-19th century. The equations also describe...

in the topic, during which Maxwell's classmate, Edward John Routh, abstracted Maxwell's results for the general class of linear systems. Independently...