Thank you!
I didn't use harmonic oscillator mostly because I didn't want to deal with its wavefunctions cause that would have taken me more time. So then that means that all transitions are allowed for particle in a box when μ=x2 until |μ|2 gets arbitrarily close to zero. Kind of weird.
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...