  We study two spinless bosons interacting via two-body Gaussian potential
subjected to an externally impressed rotation about an axis confined in a
harmonic trap in two-spatial dimensions. We obtain a transcendental equation
for the relative angular momentum $|m|$ state with various values of the
two-body interaction range $\sigma$ and the two-body interaction strength
$g_{2}$ to study the resulting energy spectrum and analyze the role of Hilbert
space dimensions $\widetilde{N}$. We compare results for both attractive and
repulsive interaction for $\delta$-function potential and Gaussian potential
for various values of interaction range. We study the effects of interaction
parameters and relative angular momentum on the ground state energy and its
various components, namely, kinetic energy, trap potential and interaction
potential. For a given $|m|$ and non-interacting case, we observe that the
ground state energy becomes independent of interaction range. However, for a
given relative angular momentum and interaction strength $g_{2}>0$, there is an
increase in ground state energy with an increase in interaction range. Below
the interaction strength $g_{2}V(r)\leq -1$, ground state energy diverges to
physically unacceptable negative-infinity for $|m|=0$ state. Further, for
$|m|=1$, the ground state energy becomes independent of the interaction
strength. For a $|m|$, we present a comparative study between the Gaussian
interaction potential and the $\delta$-function potential. Further, we observe
that for a given $g_{2}$ and $|m|$, for $\delta$-function potential {\it i.e.}
$\sigma\to 0$, to achieve the convergence of ground state energy, we require a
considerably large critical Hilbert space. Whereas, in the case of Gaussian
interaction potential with $\sigma\to 1$, the ground state energy converges for
a considerably small critical Hilbert space.
