The present theory of accommodation and adsorption of atoms on solid surfaces is re-examined, and the consequences of a more exact quantum treatment are explored. Using the system He-W as an illustrative example, it is shown that the disturbing qualitative features of the quantum results, that is the well-known qualitative disagreement of the results with both intuition and experimental trends at low energies, are still present. The precise physical reasons for the qualitative behavior of the theoretical results are examined in detail, and are made clear. With these reasons clarified and understood, it is concluded that there is no hope of bringing the conventional quantum theory into agreement with the expected trends, and that further theoretical progress will be difficult without results of certain future experiments. Effects of dimensionality of the (continuum) solid model are examined: it is shown that the situation is improved slightly if a two-dimensional model (surface modes?), as opposed to the conventional three-dimensional model (bulk modes) is used; use of a one-dimensional model considerably improves the situation, but this is presumably irrelevant to the real processes involved.