  We examine the problem of two particles confined in an isotropic harmonic
trap, which interact via a finite-ranged Gaussian-shaped potential in two
spatial dimensions. We derive an approximative transcendental equation for the
energy and study the resulting spectrum as a function of the interparticle
interaction strength. Both the attractive and repulsive systems are analyzed.
We study the impact of the potential's range on the ground-state energy.
Complementary, we also explicitly verify by a variational treatment that in the
zero-range limit the positive delta potential in two dimensions only reproduces
the non-interacting results, if the Hilbert space in not truncated. Finally, we
establish and discuss the connection between our finite-range treatment and
regularized zero-range results from the literature.
