  We investigate consequences of space non-commutativity in quantum mechanics
of the hydrogen atom. We introduce rotationally invariant noncommutative space
$\hat{\bf R}^3_0$ - an analog of the hydrogen atom ($H$-atom) configuration
space ${\bf R}^3_0\,=\, {\bf R}^3\setminus \{0\}$. The space $\hat{\bf R}^3_0$
is generated by noncommutative coordinates realized as operators in an
auxiliary (Fock) space ${\cal F}$. We introduce the Hilbert space
$\hat{\cal{H}}$ of wave functions $\hat{\psi}$ formed by properly weighted
Hilbert-Schmidt operators in ${\cal F}$. Finally, we define an analog of the
$H$-atom Hamiltonian in $\hat{\bf R}^3_0$ and explicitly determine the bound
state energies $E^\lambda_n$ and the corresponding eigenstates
$\hat{\psi}^\lambda_{njm}$. The Coulomb scattering problem in $\hat{\bf R}^3_0$
is under study.
