  The spontaneous emission rate of excitons strongly confined in quantum dots
is proportional to the overlap integral of electron and hole envelope wave
functions. A common and intuitive interpretation of this result is that the
spontaneous emission rate is proportional to the probability that the electron
and the hole are located at the same point or region in space, i.e. they must
coincide spatially to recombine. Here we show that this interpretation is not
correct even loosely speaking. By general mathematical considerations we
compare the envelope wave function overlap, the exchange overlap integral, and
the probability of electrons and holes coinciding and find that the frequency
dependence of the envelope wave function overlap integral is very different
from that expected from the common interpretation. We show that these
theoretical considerations lead to predictions for measurements. We compare our
qualitative predictions with recent measurements of the wave function overlap
and find good agreement.

Mesoscale and Nanoscale Physics;Other Condensed Matter