My instructor was talking about allowed transitions for IR spectroscopy and how you can predict them relatively well using PIB wavefunctions. It was stated that you could solve for the probability of a transition moment to determine if a transition is forbidden or not. <μ>=∫ΨfμΨidτ where μ=x So for fun I plugged in μ=x2 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?