Exact results of a hard-core interacting system with a single impurity
  The quantum-mechanical problem of a many-particle system with a single impurity in one-dimension, interacting by a delta-function, is solved. The wave-function for a bosonic system and the related secular equation for the spectrum are obtained. The energy per length is calculated in the thermodynamic limit. 
You-Quan Li and Zhong-Shui Ma