Solving the quantum nonlinear Schrodinger equation with delta-type impurity
- Publisher: American Institute of Physics
QC | Mathematical Physics | High Energy Physics - Theory | Mathematics - Quantum Algebra | 82B23, 81R50
We establish the exact solution of the nonlinear Schrodinger equation with a delta-function impurity, representing a pointlike defect which reflects and transmits. We solve the problem both at the classical and the second quantized levels. In the quantum case the Zamolodchikov-Faddeev algebra, familiar from the case without impurities, is substituted by the recently discovered reflection-transmission (RT) algebra, which captures both particle-particle and particle-impurity interactions. The off-shell quantum solution is expressed in terms of the generators of the RT algebra and the exact scattering matrix of the theory is derived. (C) 2005 American Institute of Physics.