Exact results of a hard-core interacting system with a single impurity

TL;DR

This paper provides an exact solution to a one-dimensional quantum many-particle system with a single impurity interacting via a delta-function, including wave-function, spectrum, and energy calculations.

Contribution

It presents the first exact analytical solution for a bosonic system with a single impurity in one dimension, including spectrum and energy results.

Findings

Wave-function for the bosonic system derived

Secular equation for the spectrum obtained

Energy per length calculated in the thermodynamic limit

Abstract

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.