  The coordinate-space wave function $\psi(x)$ of quasi-one-dimensional atoms
is defined in the $x\geq 0$ region only. This poses a typical problem to write
a physically acceptable momentum-space wave function $\phi(p)$ from the Fourier
transform of $\psi(x)$. We resolve the problem with special attention to the
behavior of real and imaginary parts of the complex-valued function $\phi(p)$
as a function of $p$ and confirm that $\phi_i(p)$ (the imaginary part of
$\phi(p)$) represents the correct momentum-space wave function. We make use of
the results for $\psi(x)$ and $\phi_i(p)$ to express the position- and
momentum-space Fisher information in terms of the principal quantum number and
energy eigen value of the system and provide some useful checks on the result
presented with particular attention on the information theoretic uncertainty
relation.
