How can Fourier analysis assist in the study of quantum systems and the analysis of wave functions?

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Fourier transformation helps investigate quantum systems and scrutinize wave function by partitioning the complicated wave function into its frequency components to reveal the connection between momentum and position, elucidating quantum particle attributes and functionalities. Since wave functions exhibit divergent characteristics between these spectrum functions, physicists can now expound on quantum mechanics' behavior and traits. Utilizing Fourier analysis helps solve the Schrodinger equation convolutely, illuminating interference, uncertainty, and superposition. This mathematical equipment triggers and elucidates quantum evolution and interactions vital for practical and theoretical quantum mechanics.

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