Recursive Method for the Density of States in One Dimension

We derive a powerful yet simple method for analyzing the local density of states (DOS) 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 power laws 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.