In this section we will discuss the wave function of the hard-rod gas, i.e. the
one-dimensional gas of impenetrable particles (1.79) of radius . Already
in his original work[Gir60], Girardeau noted that the exact ground
state wave function of a hard-rod system can be obtained from the wave function of the
TG gas (Sec 2.5.4.1) by subtracting the excluded volume. That can be done by
the transformation
This exact wave function is used for calculation of correlation properties in the super-Tonks regime.