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One person suggested to me that it makes sense to change the sign of k
because that's proportional to momentum, whereas it doesn't make sense to
change the sign of w because that's a frequency. For a complex wave, he
suggested we like to keep the sign of the exp(iwt) term alone and only
fiddle with the sign of the exp(ikx) piece.
Do you agree with that suggestion?
Is there another way to look at this situation?