How will these hydrogen atoms interact?
How one atom interact with another atom is an difficult question and requires quite some calculations, even for a system with only two hydrogen atoms.  Basically, this is done by solving the Schrödinger equation for the system.  The answer will also depend on the electronics state of the system, especially the spin state.

If the system is in a triplet electronic state, the two atom will experience a repulsive force that approach infinity as you pull the two atoms closer, and that force approaches zero as the distance approaches infinity.

If the system is in a singlet state, the force is zero at the equilibrium bond length of $H_2$ atom(~0.74Å).  As the distance gets smaller the atoms experience an increasing repulsive force which approaches infinity at 0.  As the two atoms are pulled apart from the equilibrium there is a decreasing attractive force that approaches 0 at infinity.