  The non-relativistic hydrogen atom and the Zwanziger problem have the same
dynamical symmetry for bound and scattering states.We show that this is also
true for a Hilbert space which is non-commutative in co-ordinates. The group
structure is described using the redefined velocity operator and Laplace
Runge-Lenz operator in terms of left and right handed representations of the
non-commutative Hilbert space $ R_{\lambda}^{3}$.The bound state algebra is
SO(4) and the scattering state algebra is SO(3,1).
