Difference between revisions of "Wave mechanics"
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| Line 12: | Line 12: | ||
k = 2π/λ | k = 2π/λ | ||
| − | w = 2πf | + | w = 2πf = 2π/T |
So if given the amplitude, wavelength and frequency of a particle that was behaving in a sine fashion, its position could be calculated at a particular time on the t axis using this equation. It would also give the particle position as a function of time at a particular distance on the x axis. Both plots F vs. x and F vs. t would be cosine plots. | So if given the amplitude, wavelength and frequency of a particle that was behaving in a sine fashion, its position could be calculated at a particular time on the t axis using this equation. It would also give the particle position as a function of time at a particular distance on the x axis. Both plots F vs. x and F vs. t would be cosine plots. | ||
Revision as of 12:02, 5 May 2020
Introduction
Basic Equation
The basic equation of wave mechanics is a function that describes the position of a particle as a function of time, where the function is wavelike, such as sine or cosine:
y(x,t) = Ψ = Asin(kx - ωt)
A = amplitude
k = 2π/λ
w = 2πf = 2π/T
So if given the amplitude, wavelength and frequency of a particle that was behaving in a sine fashion, its position could be calculated at a particular time on the t axis using this equation. It would also give the particle position as a function of time at a particular distance on the x axis. Both plots F vs. x and F vs. t would be cosine plots.
