Spherical wave transformations leave the form of spherical waves as well as the laws of optics and electrodynamics invariant in all inertial frames. They...

transformation of indefinite quadratic forms, squeeze mappings of the hyperbola, group theory, Möbius transformations, spherical wave transformation,...

linear fractional transformations that is not affine. In mathematical physics, certain conformal maps known as spherical wave transformations are special conformal...

equations. They called a generic expression of conformal symmetry a spherical wave transformation. General relativity in two spacetime dimensions also enjoys...

Lorentz transformation is not the only transformation leaving invariant the shape of spherical waves, as there is a wider set of spherical wave transformations...

} William Thomson, 1st Baron Kelvin Inversive geometry Spherical wave transformation William Thomson, Lord Kelvin (1845) "Extrait d'une lettre de...

scientific fields. The table of spherical harmonics contains a list of common spherical harmonics. Since the spherical harmonics form a complete set of...

}}}x\right)}} where n = 0, 1, 2, .... The wave functions of an electron in a Hydrogen atom are expressed in terms of spherical harmonics and generalized Laguerre...

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that...

 303–310 (1921). Acceleration (special relativity) Möbius transformation Spherical wave transformation Squeeze mapping Rindler coordinates "DigiArchiv of SRA...

by the extraordinarily small effect the waves would produce on a detector. The amplitude of a spherical wave will fall off as the inverse of the distance...

produces secondary circular waves emanating from the lighthouse, so an X-ray striking an electron produces secondary spherical waves emanating from the electron...

In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion...

class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates...

In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the VSH...

independent variable. In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian...

denoted by Ak. The set Ak consists of the solid spherical harmonics of degree k. The solid spherical harmonics play a similar role in higher dimensions...

inversive geometry into electromagnetic theory with their transformations (spherical wave transformation): Each four-dimensional solution [to Maxwell's equations]...

the Lorentz group. Bateman called the elements of this group spherical wave transformations. In evaluating this paper, one of his students, Clifford Truesdell...

fractional transformations on the projective line over that ring. Elements of the spacetime conformal group were called spherical wave transformations by Bateman...

unitary transformation of both factors simultaneously and since transformation of complex spherical harmonics to real form is by a unitary transformation, we...

isolated atom. The transformation T {\displaystyle {\mathcal {T}}} is thus specified by three quantities: a set of all-electron partial waves | ϕ i ⟩ {\displaystyle...

he also discussed the conformal spacetime transformations (related to the spherical wave transformation by Harry Bateman and Ebenezer Cunningham in...

the effect of a Galilean transformation upon the Schrödinger equation can be canceled by a phase transformation of the wave function that leaves the probabilities...

In Hamiltonian mechanics, the linear canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms. It has...

isolated spherically symmetric object. (See also the article on plane wave spacetimes for a discussion of physically important special cases of plane waves.)...

related to 3-dimensional spherical harmonics. These shapes are not unique, and any linear combination is valid, like a transformation to cubic harmonics, in...

indistinguishable from a black hole formed by the collapse of a spherical mass. In its transition to a spherical shape, the black hole formed by the collapse of a more...

and multivariate calculus coordinate systems (rectangular, cylindrical, spherical) vector algebra and vector differential operators Fourier series partial...

Hypercone Light-cone coordinates Lorentz transformation Method of characteristics Minkowski diagram Monge cone Wave equation Cox, Brian; Forshaw, J. R. (2009)...