How Do You Prove the Second Formula Using the First?

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SUMMARY

The discussion focuses on proving the second formula using the first formula by rewriting the dot product in terms of magnitudes and angles. Participants suggest defining the q-vector along the z-hat direction to simplify the process. The use of spherical coordinates is emphasized as a crucial step in the proof. This method provides a clear pathway to establish the relationship between the two formulas effectively.

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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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