Exact analysis of an interacting bose gas. I. the general solution and the ground state

A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the solutions of a transcendental equation. The problem has one nontrivial coupling constant,. When is small, Bogoliubov's perturbation theory is seen to be valid. In this paper, we explicitly calculate the ground-state energy as a function of and show that it is analytic for all, except =0. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrum not one as is ordinarily supposed.