  In this work we study a system of two distinguishable fermions in a 1D
harmonic potential. This system has the exceptional property that there is an
analytic solution for arbitrary values of the interparticle interaction. We
tune the interaction strength via a magnetic offset field and compare the
measured properties of the system to the theoretical prediction. At the point
where the interaction strength diverges, the energy and square of the wave
function for two distinguishable particles are the same as for a system of two
identical fermions. This is referred to as fermionization. We have observed
this phenomenon by directly comparing two distinguishable fermions with
diverging interaction strength with two identical fermions in the same
potential. We observe good agreement between experiment and theory. By adding
one or more particles our system can be used as a quantum simulator for more
complex few-body systems where no theoretical solution is available.
