Abstract
Abstract
We study the exact solutions for a one-dimensional system of N = 2; 3 spinless point bosons for zero boundary conditions. In this case, we are based on M Gaudin’s formulae obtained with the help of Bethe ansatz. We find the density profile ρ(x) and the nodal structure of a wave function for a set of the lowest states of the system for different values of the coupling constant γ ⩾ 0. The analysis shows that the ideal crystal corresponds to the quantum numbers (from Gaudin’s equations) n
1 = ⋯ = n
N
= N and to the coupling constant γ ≲ 1. We also find that the ground state (GS) of the system (n
1 = ⋯ = n
N
= 1) corresponds to a liquid for any γ and any N ≫ 1. In this case, the wave function of the GS is nodeless, and the wave function of the ideal crystal has nodes.
Funder
The National Academy of Sciences of Ukraine grant ‘Effects of external fields and spatial inhomogeneities on the electronic properties of Dirac and superconducting materials’
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
1 articles.
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