Difference between revisions of "Wave mechanics"
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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: | 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: | ||
| − | F(x,t) = Ψ = | + | F(x,t) = Ψ = Asin(kx - ωt) |
| − | image showing | + | image showing sine on F,x and t 3d plot labelled with A, k and ω. |
A = amplitude | A = amplitude | ||
| Line 14: | Line 14: | ||
w = 2πf | w = 2πf | ||
| − | So if given the amplitude, wavelength and frequency of a particle that was behaving in a | + | 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 11:52, 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:
F(x,t) = Ψ = Asin(kx - ωt)
image showing sine on F,x and t 3d plot labelled with A, k and ω.
A = amplitude
k = 2π/λ
w = 2πf
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.
