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<μ>=∫Ψ

_{f}μΨ

_{i}dτ where μ=x

So for fun I plugged in μ=x

^{2}and started getting alternating negative and positive, whose absolute values decreased as the difference between i and f increased. The integral value never reached zero.

I'm mostly wondering what a negative transition moment means, my gut tells me emission. And can there be any transitions which are forbidden if the integral value is never zero?