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For a harmonically trapped system consisting of two bosons in one spatialdimension with infinite contact repulsion (hard core bosons), we derive anexpression for the one-body density matrix $\rho_B$ in terms of centre of massand relative coordinates of the particles. The deviation from $\rho_F$, thedensity matrix for the two fermions case, can be clearly identified. Moreover,the obtained $\rho_B$ allows us to derive a closed form expression of thecorresponding momentum distribution $n_{B}(p)$. We show how the result deviatesfrom the noninteracting fermionic case, the deviation being associated to theshort range character of the interaction. Mathematically, our analyticalmomentum distribution is expressed in terms of one and two variables confluenthypergeometric functions. Our formula satisfies the correct normalization andpossesses the expected behavior at zero momentum. It also exhibits the highmomentum $1/p^4 $ tail with the appropriate Tan's coefficient. Numericalresults support our findings.

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical