Would atomic oxygen and atomic hydrogen result in O2 and H2 only, or some H2O too? Let's assume we have atomic oxygen and atomic hydrogen in a closed chamber, the temperature and pressure of which we're able to monitor (and control). Number of hydrogen atoms are twice that of oxygen.

Would this result in spontaneous formation of:


$\ce{O2}$ and $\ce{H2}$ only?
$\ce{O2}$ and $\ce{H2}$ with some $\ce{H2O}$?
and how would the process vary with temperature and pressure?
And I assume creating mostly $\ce{H2O}$ is the hardest (though I would be interested in a comment on this as well).


and how could one carry out analysis on paper to figure out what would happen? (I'm from a physics background, and my chemistry knowledge is a bit rusty. Though I do have a good background on thermodynamics, enthalpy, Helmholtz free, Gibbs free energies, etc, etc).

For the sake of brevity and focus of this question, we can ignore the question of how atomic oxygen and hydrogen came about in the first place. (This assumption is even more acceptable in the special case of carrying out molecular dynamics computer simulation, something I'm interested in, because we don't have to worry about how to form atomic $\ce O$ and $\ce H$)

edit: I guess I should clarify that I'm interested in a first principles analysis of this problem (since I'm mainly interested in MD). Also what if we had two other species of atomic gases (Ar and Ne, Ar and O, Ar and H, etc, etc). I think I'm more interested in it from a physical chemistry point of view (though without quantum mechanics if possible).
It would ignite and form water vapor. It's not complicated to figure out. The conditions you have described with a mixture of monoatomic hydrogen and oxygen is what is formed when a spark passes through a mixture of hydrogen and oxygen gases.