Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
Abstract
A gas of onedimensional Bose particles interacting via a repulsive deltafunction 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, γ. When γ is small, Bogoliubov's perturbation theory is seen to be valid. In this paper, we explicitly calculate the groundstate energy as a function of γ and show that it is analytic for all γ, except γ=0. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrumnot one as is ordinarily supposed.
 Publication:

Physical Review
 Pub Date:
 May 1963
 DOI:
 10.1103/PhysRev.130.1605
 Bibcode:
 1963PhRv..130.1605L