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The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
Among the textbooks published after Jackson's book, Julian Schwinger's 1970s lecture notes is a mentionable book first published in 1998 posthumously. Due to the domination of Jackson's textbook in graduate physics education, even physicists like Schwinger became frustrated competing with Jackson and because of this, the publication of ...
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves).
Finally only in this case the superposition principle fully apply, i.e. the wave function in a point P can be expanded as a superposition of waves on a border surface enclosing P. Wave functions can be interpreted in the usual quantum mechanical sense as probability densities where the formalism of Green's functions and propagators apply. What ...
The concept of universal wavefunction was introduced by Hugh Everett in his 1956 PhD thesis draft The Theory of the Universal Wave Function. [8] It later received investigation from James Hartle and Stephen Hawking [ 9 ] who derived the Hartle–Hawking solution to the Wheeler–deWitt equation to explain the initial conditions of the Big Bang ...
Kinematic wave can be described by a simple partial differential equation with a single unknown field variable (e.g., the flow or wave height, ) in terms of the two independent variables, namely the time and the space with some parameters (coefficients) containing information about the physics and geometry of the flow. In general, the wave can ...
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In physics, the acoustic wave equation is a second-order partial differential equation that governs the propagation of acoustic waves through a material medium resp. a standing wavefield. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position x and time t .