Abstract
One-dimensional Bose gases are considered, interactingeither through the hard-core potentials or through the contactdelta potentials. Interest in these gases gained momentum becauseof the recent experimental realization of quasi-one-dimensionalBose gases in traps with tightly confined radial motion, achievingthe Tonks-Girardeau (TG) regime of strongly interacting atoms. Forsuch gases the Fermi-Bose mapping of wavefunctions is applicable.The aim of the present communication is to give a brief survey ofthe problem and to demonstrate the generality of this mapping byemphasizing that: (i) It is valid for nonequilibriumwavefunctions, described by the time-dependent Schrödingerequation, not merely for stationary wavefunctions. (ii) It givesthe whole spectrum of all excited states, not merely the groundstate. (iii) It applies to the Lieb-Liniger gas with the contactinteraction, not merely to the TG gas of impenetrable bosons.
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