Two-particle system in Coulomb potential for twist-deformed space-time

In this article, we define two-particle system in Coulomb potential for twist-deformed space-time with spatial directions commuting to time-dependent function $f_{\kappa_a}({t})$. Particularly, we provide the proper Hamiltonian function and further, we rewrite it in terms of commutative variables. Besides, we demonstrate, that for small values of deformation parameters, the obtained in the perturbation framework, first-ordered corrections for ground Helium energy are equal to zero. In such a way we show, that nontrivial impact of space-time noncommutativity appears only at the second order of the quantum-mechanical correction expansion.