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Expected value of momentum and Fourier transform

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The expected value of the momentum operator in quantum mechanics can be calculated using the spatial wave function. Using that the momentum wave function is the Fourier transform of the spatial wave function we obtain an expression for this expected value in term of the momentum wave function, that is, we prove the Equation 15.64 in the attached file.

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Solution Summary

Given that a spatial wave function, its Fourier transform gives the momentum wave function. We explain that properties of the Fourier transform can be used to find an expression for the expected value of the momentum using the momentum wave function

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