Why can't the wavefunction equal infinity?

[LogicX]

I see why having mutiple points of infinity in the wavefunction would be bad. But what about one point being infinity and everywhere else being zero? Is this the only case where the wavefunction could have an infinite value?

Would this be a case where the expectation value of whatever physical quantity you are measuring is the same every time you measure it?

 

[bhobba]

I see why having mutiple points of infinity in the wavefunction would be bad. But what about one point being infinity and everywhere else being zero? Is this the only case where the wavefunction could have an infinite value?

Would this be a case where the expectation value of whatever physical quantity you are measuring is the same every time you measure it?

Yea - its called the Dirac Delta function. And it is remains in that state - yes - it will always give that position.

Thanks
Bill

 

[tom.stoer]

It depends which Hilbert space is used to describe the system. The Dirac delta function is a well-known exampole - and you can even add several delta functions. Of course these delta functions are no longer square integrable!

In principle when starting with an L² Hilbert space a singularity is no problem as long as the wave function remains square integrable. But we are doing physics, not mathematics, so the question is whether there is a physical system where such a behavior makes sense.