https://doi.org/10.1140/epjp/s13360-021-01671-x
Regular Article
The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical
1
Département de Physique. Laboratoire de physique quantique et systèmes dynamiques, Université Ferhat Abbas Sétif-1, 19000, Setif, Algeria
2
Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain
3
UMR 7019, LPCT, Université de Lorraine-CNRS, 57000, Metz, France
b
luismiguel.nieto.calzada@uva.es
Received:
6
March
2021
Accepted:
13
June
2021
Published online:
6
July
2021
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 
in terms of center of mass and relative coordinates of the particles. The deviation from 
, the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained allows us to derive a closed form expression of the corresponding momentum distribution 
. We show how the result deviates from the noninteracting fermionic case, the deviation being associated with 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 
tail with the appropriate Tan’s coefficient. Numerical results support our findings.
© The Author(s) 2021
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