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The coordinate-space wave function $\psi(x)$ of quasi-one-dimensional atomsis defined in the $x\geq 0$ region only. This poses a typical problem to writea physically acceptable momentum-space wave function $\phi(p)$ from the Fouriertransform of $\psi(x)$. We resolve the problem with special attention to thebehavior 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 ofthe results for $\psi(x)$ and $\phi_i(p)$ to express the position- andmomentum-space Fisher information in terms of the principal quantum number andenergy eigen value of the system and provide some useful checks on the resultpresented with particular attention on the information theoretic uncertaintyrelation.

Fisher information for quasi-one-dimensional hydrogen atom