We will now re-introduce the time dependence for real traveling waves. Below you will see one of the localized wave packets that we studied in Section 2c. It is found by adding ±0.05,0.1,0.15,0.2*k to the fundamental. Each component has an amplitude of 1.
Dispersion is the manner in which the frequency and the wave number are related in a medium.
Light waves have a linear dispersion in a vacuum but in water they have a nonlinear dispersion. This nonlinear dispersion can cause a white light spectrum to be changed into a rainbow. For light in a vacuum, every frequency travels at the same speed, c. E = pc = ħkc = ħw . w = kc. The index of refraction of visible light in glass has a component that varies as a k2, to a first approximation. Thus, visible light in glass has an inverse dispersion relation. w = w(1/k)
The probability density function, Psi(x,t), for massive particles has a nonlinear, quadratic dispersion. E = ħw = p2/2m. w = ħk2/2m.
Each point along the x-axis oscillates in a complicated (non-sinusoidal) manner. Before we complete this Section, write the time dependent function for the linear dispersion wave used in this Section. Now go to the remaining part by clicking on Initialize.
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