In this section we will describe the construction of the trial wave function
used fir the investigation of the super-Tonks system (see
Chapter 6).
We use Bijl-Jastrow construction (2.37) with the two-body term which is
chosen to be similar to (2.51)
The cut-off length is a variational parameter, while the wave vector
(for
a given
) is chosen in a such way that the boundary condition imposed by the
-function potential (2.52) at
is satisfied:
. For distances smaller than the cut-off length,
,
the above wave function corresponds to the exact solution with positive energy of
the two-body problem with the interaction potential
(see,
formula 1.65).