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