Hard-rod wave function (exact)

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 $a_{1D}$. 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

$$z_i' = z_i - ia_{1D},\qquad i=\overline{1,N}$$ (2.47)

This exact wave function is used for calculation of correlation properties in the super-Tonks regime.