The general idea of finite size scaling are tested by the example of t
he pure quantum version of an exactly solvable model of structural pha
se transition with long-range interaction decaying at large distances
r as r(-d-sigma), where d is the space dimensionality and sigma > 0. T
he finite size shift of the quantum parameter (playing the same role a
s that of the temperature for classical systems) is calculated for the
general geometry L(d-d') x infinity(d'), with 0 < d' < d. The root me
an square order parameter is evaluated for 0 < d' < sigma/2.