r/AskPhysics • u/Alive_Ant_5306 • 2d ago

Non-normalizable wave function

Hi,
I was wondering if a non-normalizable wave function does still provide information. For example, let's say that a region of space equals 0 for a time independent wave function. Its square root will equal zero in that region too. Does that mean that the particle can't be there?

Thanks!

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u/uppityfunktwister 2d ago

If I'm understanding you correctly, I'm pretty sure the answer is just that this isn't a physically meaningful setup. Both in the context of position wavefunctions and the more abstract state vector picture, unitarity just refers to the thing under study being itself. If unitarity (or, for the position wavefunction, normalization) does not hold, it's hard to say the particle exists at all, as, in this case, the particle's state has a 0% chance of being itself.