We investigate degenerate quantum gases in one dimension trapped in a
harmonic potential that is split in the centre by a pointlike potential. Since
the single particle eigenfunctions of such a system are known for all strengths
of the central potential, the dynamics for non-interacting fermionic gases and
low-density, strongly interacting bosonic gases can be investigated exactly
using the Fermi-Bose mapping theorem. We calculate the exact many-particle
ground-state wave-functions for both particle species, investigate soliton-like
solutions, and compare the bosonic system to the well-known physics of Bose
gases described by the Gross-Pitaevskii equation. We also address the
experimentally important questions of creation and detection of such states.Comment: 7 pages, 5 figure
