We reduce the two-body problem to the one-body problem in the general case of a deformed Heisenberg algebra leading to minimal length. Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain an analytical expression for the energy spectrum for partial cases of deformation function. The dependence of the energy spectrum on the center-of-mass momentum is found. For the special case of deformation function, which corresponds to a cutoff procedure in momentum space, it is shown that this dependence is more likely to be observed for identical particles.
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