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We investigate the lowest scattering state of one-dimensional Bose gas withattractive interactions trapped in a hard wall trap. By solving the Betheansatz equation numerically we determine the full energy spectrum and the exactwave function for different attractive interaction parameters. The resultantdensity distribution, momentum distribution, reduced one body density matrixand two body correlation show that the decreased attractive interaction inducesrich density profiles and specific correlation properties in the weaklyattractive Bose gas.

The lowest scattering state of one-dimensional Bose gas with attractive interactions