  To calculate static response properties of a many body system, local density
approximation (LDA) can be safely applied. But applicability of LDA is limited
for the case of dynamical response functions since dynamics of the system needs
to be considered as well. To examine this in the context of cold atoms, we
consider a system of non-interacting spin-$1/2$ fermions confined by a harmonic
trapping potential. We have calculated a very important response function, the
spectral intensity distribution function (SIDF), both exactly and using LDA at
zero temperature and compared with each other for different dimensions, trap
frequencies and momenta. The behavior of the SIDF at a particular momentum can
be explained by noting the behavior of the density of states (DOS) of the free
system (without trap) in that particular dimension. The agreement between exact
and LDA SIDFs becomes better with increase in dimensions and number of
particles.
