Infinite wave train for an electron?

1. Sep 9, 2003

Sacroiliac

The normalization of the free (say, electron) in quantum mechanics is
achieved by a trick with the dirac delta function. Typically we write the
orthogonality conditions for u1=c*exp(i*k1*x) and u2=c*exp(i*k2*x) as:

int(u1*u2)=delta(k1-k2)

and then out pops the nomalization constant c=1/sqrt(2*pi*hbar). This is
great and all, but what does it mean - we still violate the normalization
condition over all but one length! So what does it mean to 'delta function
normalize'? There are numerous other simialr situations which lead to the
same kind of issue.

Any thoughts?

Thanks