How Do You Prove the Second Formula Using the First?

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To prove the second formula using the first, start by rewriting the dot product in the exponential of the first formula in terms of known quantities, specifically magnitudes and angles. Define the q-vector along the z-hat direction to simplify calculations. Next, express the measure in spherical coordinates to facilitate the proof. This approach allows for a clearer transition from the first to the second formula. Following these steps will lead to a successful demonstration of the relationship between the two formulas.
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can you tell me how to prove the second formula according to the first formula in the attachment?
 

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In the exponential of the first formula, rewrite the dot product in terms of things you know (magnitudes and angles) by picking/defining your q-vector to be along the z-hat direction. After that, write the measure in spherical coordinates and run with it.
 
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