  Two identical non-interacting fermions in a three-dimensional harmonic
oscillator well are bosonised exactly according to a recently developed general
algebraic scheme. Rotational invariance is taken into account within the scheme
for the first time. The example is generic for the excitation spectra of finite
systems, in particular for the appearance of bands in spectra. A connection to
the formalism of the fractional quantum Hall effect is pointed out.
