What is Normalization?

[totentanz]

I just want to ask this: what is the physical meaning of wavefunction's normalization?
thanks for everyone in advance

[Hurkyl]

AFAIK, there isn't one. I have never seen someone give a physical meaning to an unnormalized wavefunction that was not identical to the physical meaning of its normalizations.

[cgk]

I second that. Normalization is used to make calculations easier; many formulas look simpler in terms of normalized wave functions. But as long as a wave function is /normalizable/, it carries the same information no matter whether it actually is normalized or not. Just the "direction" matters (the ray it is on).

[oraclelive]

For instance, consider an atom in a single electron (such as Hydrogen or ionized Helium), if the wavefunction is normalized (which it does for the electron to exist), the wavefunction of the electron completely describe the way the electron behaves in an atom-like the energy and momentum associated with the behaviour.

[totentanz]

For instance, consider an atom in a single electron (such as Hydrogen or ionized Helium), if the wavefunction is normalized (which it does for the electron to exist), the wavefunction of the electron completely describe the way the electron behaves in an atom-like the energy and momentum associated with the behaviour.

But I think that this makes the second form of Heisenberg Principle unconsistant...what do you think?

[xienohp]

Normalizable => Follows conservation of probability => theoretically exist given state

[vanhees71]

A wave function that is not normalizable does not represent a state in quantum theory. E.g., the plane-wave solutions of the free Schrödinger equation are not representing states. They belong to the dual space of the dense sub space where position and momentum operators are defined. Have a look on "rigged Hilbert space", e.g., in Ballentines excellent textbook on quantum mechanics.