Furthermore, every quantum `particle' has an associated, 'de Broglie wave', which is called the wave-particle duality in quantum theory; for example, electrons, protons, neutrons, quarks, neutrinos, and all other sub-atomic or elementary `particles' have their 'own' associated waves whose wavelength is inversely proportional to their energy (viz. de Broglie). The waves are represented as solutions of such differential equations, often with specified boundary conditons; thus a wave has both an amplitude and a phase.
Thus, any oscillation has a resulting, or corresponding wave that propagates; alternatively, a wave can also be represented as a continuous sequence of local oscillations of a propagating field. The intensity of the propagated signal or field is proportional to the square of the amplitude of the wave, whereas the phase can be thought of as the time interval that has elapsed from the beginning of the wave propagation to the point in space where its phase is determined or measured. There are two basic types of waves: longitudinal (for example, in an elastic medium such as sounds and sea waves)-that are propagating via longitudinal oscillations of particles in the elastic medium which occur along the direction of propagation of the wave front, or transversal waves (for example, electromagnetic) that can also propagate in vacuum.
Because of the periodic nature of the waves and of their propagation, wave superposition is readily analyzed in terms of either Fourier series or integrals. General solutions of the wave equations are thus usually expressed in terms of Fourier series whose components are `monochromatic' (single- frequency) waves.
where
As of this snapshot date, this entry was owned by bci1.