  We investigate a system of $N$ spinless bosons confined in
quasi-two-dimensional harmonic trap with repulsive two-body finite-range
Gaussian interaction potential of large $s$-wave scattering length. Exact
diagonalization of the Hamiltonian matrix is carried out to obtain the $N$-body
ground state as well as low-lying excited states, using Davidson algorithm in
beyond lowest-Landau-level approximation. We examine the finite-range effects
of the interaction potential on the many-body ground state energy as also the
degree of condensation of the Bose-condensed gas. The results obtained indicate
that the finite-range Gaussian interaction potential enhances the degree of
condensation compared to the zero-range interaction potential. We further
analyze the effect of finite-range interaction potential on the breathing mode
collective excitation. Our theoretical results may be relevant for experiments
currently conducted on quasi-two-dimensional Bose gas with more realistic
interaction potential.
