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We investigate a two-body quantum system with hard-core interaction potentialin a two-dimensional harmonic trap. We provide the exact analytical solution ofthe problem. The energy spectrum of this system as a function of the range ofthe interaction reveals level crossings which can be explained examining thepotential and kinetic part of the energy, as well as the localization andoscillatory properties of the wavefunctions quantified by the Fisherinformation. The latter is sensitive to the wavefunction localization betweennodes promoting this property as a resource of quantum correlations ininteracting particle systems.

Level crossings and Fisher information of two hard-core bosons in a two-dimensional trap