InterviewSolution
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InterviewSolution
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What Is This Gaussian Business? |
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Answer» The GAUSSIAN shaped wavepacket is just one possible wave shape. We chose it to represent a localized but travelling wave packet because it MINIMISES the uncertainty product of Δx and Δk. For the Gaussian, the contribution of a given value of k to the wave packet is PROPORTIONAL to exp [-α2(k - ko)2] where α and ko are constants. This FACTOR times some constant is the function a(k). Then the wave packet function is just the integral ψ(x, t) = ∫∞-∞ a(k)EI(kx−wt) dk The Gaussian shaped wavepacket is just one possible wave shape. We chose it to represent a localized but travelling wave packet because it minimises the uncertainty product of Δx and Δk. For the Gaussian, the contribution of a given value of k to the wave packet is proportional to exp [-α2(k - ko)2] where α and ko are constants. This factor times some constant is the function a(k). Then the wave packet function is just the integral ψ(x, t) = ∫∞-∞ a(k)ei(kx−wt) dk |
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