Because the 
are pure states with respect to momentum, we
expect to find find complete
uncertainty
in position. Indeed, the probability distribution associated with
these functions is constant in space,
Strictly speaking, in an infinite space, these functions are not normalizable,
However, this form of unnormalizability is much milder than that of
the exponentially growing wave functions and is manageable. We may
imagine placing our experiment in an extremely large box of size L.
For sufficiently large L (several billion light years, for
instance), we do not expect such a box to affect the small scale
physics we study in quantum mechanics. And, as long as L is finite,
the states will be normalizable. We thus accept our plane
wave solutions as physical, realizing that they are an
idealization in much the same way as is the idea of a an infinite
straight line.
Although we cannot insist on the normalization condition 
, it is still useful at times to have a normalization
convention for such states. We will discuss such a convention when we
turn to our general discussion of scattering in 3.
