Ground state and excitations of a one-dimensional bose gas on a finite interval

The Bethe ansatz is used to obtain the wave function of a one-dimensional bounded system of Bose particles interacting with one another through a two-body $\delta$-function potential. The interaction of the particles with the surface (the boundaries of the interval) is described by a zero-range potential. Expressions are obtained for the ground-state energy and for the spectrum of surface excitations.