  We report the plausibility of using quantum mechanical transitions, induced
by the combined effect of Gravitational wave (GW) and noncommutative (NC)
structure of space, among the states of a 2-dimensional harmonic oscillator, to
probe the spatial NC geometry. The phonon modes excited by the passing GW
within the resonant bar-detector are formally identical to forced harmonic
oscillator and they represent a length variation of roughly the same order of
magnitude as the characteristic length-scale of spatial noncommutativity
estimated from the phenomenological upper bound of the NC parameter. This
motivates our present work. We employ various GW wave-forms that are typically
expected from possible astronomical sources. We find that the transition
probablities are quite sensitive to the nature of polarization of the GW. We
also elaborate on the particular type of sources of GW, radiation from which
can induce transitions that can be used as effective probe of the spatial
noncommutative structure.
