  We study the effects of the effective range of interaction on the eigenvalues
and eigenstates of two particles confined in a three-dimensional (3D) isotropic
as well as one- or quasi-one dimensional harmonic (1D) traps. For this we
employ model potentials which mimic finite-range s-wave interactions over a
wide range of s-wave scattering length $a_s$ including the unitarity limits
$a_s \rightarrow \pm\infty$. Our results show that when the range is larger
than the 3D or 1D harmonic oscillator length scale, the eigenvalues and
eigenstates are nearly similar to those of noninteracting two particles in the
3D or 1D trap, respectively. In case of 3D, we find that when the range goes to
zero, the results of contact potential as derived by Busch {\it et al.}
[Foundations of Physics, {\bf28}, 549 (1998)] are reproduced. However, in the
case of 1D, such reproducibility does not occur as the range goes to zero. We
have calculated the eigenvalues and eigenstates in 1D harmonic trap taking
one-dimensional finite- range model potential. We have also calculated bound
state properties of two particles confined in a highly anisotropic quasi-1D
trap taking three-dimensional finite-range model potential, and examined
whether these quasi-1D results approach towards 1D ones as the aspect ratio
$\eta$ of the radial to axial frequency of the trap increases. We find that if
the range is very small compared to the axial size of the trap, then one can
reach 1D regime for $\eta \ge 10000$. However, for large range, one can nearly
get 1D results for smaller values of $\eta$. This study will be important for
exploration of two-body or many body physics of trapped ultracold atoms
interacting with narrow Feshbach resonance for which the effective range can be
large.
