  We derive a powerful yet simple method for analyzing the local density of
states in gapless one dimensional fermionic systems, including extensions such
as momentum dependent interaction parameters and hard-wall boundaries. We study
the crossover of the local DOS from individual density waves to the well-known
asymptotic powerlaws and identify characteristic signs of spin charge
separation in possible STM experiments. For semi-infinite systems a closed
analytic expression is found in terms of hypergeometric functions.
