  The ground state energy of a scale symmetric system usually does not possess
any lower bound, thus making the system quantum mechanically unstable.
Self-adjointness and renormalization techniques usually provide the system a
scale and thus making the ground state bounded from below. We on the other hand
use noncommutative quantum mechanics and exploit the noncommutative parameter
\Theta as a scale for a scale symmetric system. The resulting Hamiltonian for
the system then allows an unusual bound state at the threshold of the energy,
E=0. Apart from the Hamiltonian \hat{H} we also compute the other two
generators of the so(2,1) algebra, the dilation \hat{D} and the conformal
generator \hat{K} in the noncommutative space. The so(2,1) algebra is not
closed in the noncommutative space, but the limit \Theta\to 0 smoothly goes to
the so(2,1) algebra restoring the conformal symmetry. We also discuss the
system for large noncommutative parameter.
