  In a double slit interference experiment, the wave function at the screen
with both slits open is not exactly equal to the sum of the wave functions with
the slits individually open one at a time. The three scenarios represent three
different boundary conditions and as such, the superposition principle should
not be applicable. However, most well known text books in quantum mechanics
implicitly and/or explicitly use this assumption which is only approximately
true. In our present study, we have used the Feynman path integral formalism to
quantify contributions from non-classical paths in quantum interference
experiments which provide a measurable deviation from a naive application of
the superposition principle. A direct experimental demonstration for the
existence of these non-classical paths is hard. We find that contributions from
such paths can be significant and we propose simple three-slit interference
experiments to directly confirm their existence.
