corresponding to wavenumbers
.
Thus the smallest posssible wavenumber,
and the "distance" (in k-space) between successive
allowed wavenumbers, is 
.
There is 
allowed "state" per 
.
Put another way, the "density" of allowed states
per unit wavenumber is
or, for this one-dimensional (1D) case,
.
Note that n > 0
k > 0.
We are drawing standing waves,
(we choose x=0 at the centre of the box, for symmetry),
for which "negative" k values have no independent meaning.