We calculate the energy-level shifts of a tightly confined trapped alkali-m
etal atom in the presence of a second trapped atom. A complete microscopic
description of the interaction energy between the two atoms is used. This a
llows us to study tightly confined atoms near a Feshbach resonance and to e
valuate the usefulness of the regularized delta-function potential approxim
ation. We present results for sodium and cesium when confined in a spherica
lly symmetric harmonic optical trap. Possible implications of the level shi
fts and collisional decoherence for quantum computing with atomic systems a
re given.