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The superposition principle, [1] also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually.
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position.
Duhamel's principle is the result that the solution to an inhomogeneous, linear, partial differential equation can be solved by first finding the solution for a step input, and then superposing using Duhamel's integral.
The superposition principle applies to any linear system, including linear systems of PDEs. A common visualization of this concept is the interaction of two waves in phase being combined to result in a greater amplitude, for example sin x + sin x = 2 sin x. The same principle can be observed in PDEs where the solutions may be real or complex ...
The solution of this equation for atoms led to the explanation of the Balmer series for atomic spectra and consequently formed a basis for all of atomic physics and chemistry. This is not the only occasion [dubious – discuss] in which Maxwell's equations have forced a restructuring of Newtonian mechanics. Maxwell's equations are ...
The WLF equation is a consequence of time–temperature superposition (TTSP), which mathematically is an application of Boltzmann's superposition principle. It is TTSP, not WLF, that allows the assembly of a compliance master curve that spans more time, or frequency, than afforded by the time available for experimentation or the frequency range ...
The principle of time-temperature superposition requires the assumption of thermorheologically simple behavior (all curves have the same characteristic time variation law with temperature). From an initial spectral window [ ω 1 , ω 2 ] and a series of isotherms in this window, we can calculate the master curves of a material which extends ...
The following may be deduced by applying the principle of superposition to two sinusoidal waves, using trigonometric identities. The angle addition and sum-to-product trigonometric formulae are useful; in more advanced work complex numbers and fourier series and transforms are used.