Limiting Value of Normalized Wave Function

While defining a well behaved wave function psi, why is it that psi must go to zero as x or and y or and z tends to +-infinity? psi must converge for it to be normalizable i.e. it must not tend to infinity. It may converge to any finite value, why should it tend only to 0?
- Gamini (age 18)
India

The integral of the absolute square of the wave function has to be 1, since it represents the total probability of the particle being somewhere. (Here we're assuming that we're discussing the spatial wave function of a single particle.) Any smooth function that fails to approach zero at infinity will obviously have an infinite integral.


Mike W.

(published on 11/07/2012)