Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State

Elliott H. Lieb and Werner Liniger
Phys. Rev. 130, 1605 – Published 15 May 1963
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Abstract

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, γ. When γ 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 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 spectrum—not one as is ordinarily supposed.

  • Received 7 January 1963

DOI:https://doi.org/10.1103/PhysRev.130.1605

©1963 American Physical Society

Authors & Affiliations

Elliott H. Lieb and Werner Liniger

  • Thomas J. Watson Research Center, International Business Machines Corporation, Yorktown Heights, New York

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Issue

Vol. 130, Iss. 4 — May 1963

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