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## Fourier TransformPeriodic functions can be expressed in their frequency domain. First, the function (let's call it f) must be square integrable (at least over the periodic interval): Then a base can be found and the function be expressed using a (continuous) linear combination: This operation is called the inverse transform . The coefficients can be calculated by: ## Delta Distribution and Fourier TransformThe Fourier Transform can also be used with the δ Distribution: First, it holds that: Proof.
This also works in the other direction (!!) Proof.
In Quantum Mechanics it is customary to instead use the momentum , in that case it's slightly different: Note that δ is ## Triple Triple IntegralsSometimes multiple integrations can be simplified by observing that: Likewise: And for Quantum Mechanics: Author: Danny (remove the ".nospam" to send) Last modification on: Sat, 04 May 2024 . |