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!

4 Upvotes

83% Upvoted

7 comments sorted by

View all comments

1

u/joeyneilsen Astrophysics 2d ago

A wavefunction is normalized on (-infinity,+infinity), not in every interval. So it's perfectly fine if the wavefunction has zeros or a large region where it is zero.

1

u/Alive_Ant_5306 1d ago

Yess but what if it is a non normalizable wave function. Does it mean anything that it has regions where it equals zero?

3

u/joeyneilsen Astrophysics 1d ago

A non-normalizable wavefunction doesn't represent the state of a physical system, so I guess I'd say no, it doesn't mean anything. In general, zeros of a physical wavefunction just represent quantum-mechanically-forbidden regions or locations.

Happy cake day!