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Fourier Transform Relations in Quantum Mechanics

Discover how to rewrite and transform equations in quantum mechanics using Fourier transform relations. Follow the steps outlined in the hint to simplify integrations and expressions. Master the method to show the desired outcome accurately.

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Fourier Transform Relations in Quantum Mechanics

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  1. Problem 5-3b Hint where I’ve let ħ,c=1. † †  i Recalling that  is a function of k, it should be primed whenk is. Again, I’ve adopted the ħ,c = 1. You should be able to rewrite the left-hand side of in the form: You will need to take the Fourier transform of both sides: d3re-iK·r d3re-iK·r e-ik·r I’ve already cancelled 1/(2p)3 from both sides Integrating over d3r introduces a delta function that simplifies the integration over d3k Next do yet ANOTHER Fourier transform: d3r'eiK'·r' d3r'e-iK'·r' e-ik·r Again already canceling 1/(2p)3 from both sides You should be able to take it from here, completing the arguments to show †

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