A bosonic multi-state two-well model

Inspired by the increasing possibility of experimental control in ultracold atomic physics we introduce a new Lax operator and use it to construct and solve models with two wells and two on well states together with its generalization for n on well states. The models are solved by the algebraic Bethe Ansatz method and can be viewed as describing two Bose-Einstein condensates allowing for an exchange interaction through Josephson tunneling. (author)