Generic example of algebraic bosonisation

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.