  We conduct a theoretical study of SU(N) fermions confined by a
one-dimensional harmonic potential. Firstly, we introduce a new numerical
approach for solving the trapped interacting few-body problem, by which one may
obtain accurate energy spectra across the full range of interaction strengths.
In the strong-coupling limit, we map the SU(N) Hamiltonian to a spin-chain
model. We then show that an existing, extremely accurate ansatz - derived for a
Heisenberg SU(2) spin chain - is extendable to these N-component systems.
Lastly, we consider balanced SU(N) Fermi gases that have an equal number of
particles in each spin state for N=2, 3, 4. In the weak- and strong-coupling
regimes, we find that the ground-state energies rapidly converge to their
expected values in the thermodynamic limit with increasing atom number. This
suggests that the many-body energetics of N-component fermions may be
accurately inferred from the corresponding few-body systems of N
distinguishable particles.
