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Results tagged with fourier-transform
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user 96114
A unitary linear operator which resolves a function on $\mathbb{R}^N$ into a linear superposition of "plane wave functions". Most often used in physics for calculating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a quantum state in position co-ordinates into one in momentum co-ordinates and contrawise. There is also a discrete, fast Fourier transform for discretised data.
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What is the Fourier transform of an infinite integral of plane waves?
I'm trying to evaluate this double-integral in the context of Quantum Mechanics. Consider $f(x)$ as
$$ f(x) = \int_{-\infty}^{\infty} \mathrm{exp} \left( \frac{-ipx}{\hbar} \right) dp $$
So $\hat f …
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