  The wave mechanics of two impenetrable hard core particles in 1-D box is
analyzed. Each particle in the box behaves like an independent entity
represented by a {\it macro-orbital} (a kind of pair waveform). While the
expectation value of their interaction, $<V_{HC}(x)>$, vanishes for every state
of two particles, the expectation value of their relative separation, $<x>$,
satisfies $<x> \ge \lambda/2$ (or $q \ge \pi/d$, with $2d = L$ being the size
of the box). The particles in their ground state define a close-packed
arrangement of their wave packets (with $<x> = \lambda/2$, phase position
separation $\Delta\phi = 2\pi$ and momentum $|q_o| = \pi/d$) and experience a
mutual repulsive force ({\it zero point repulsion}) $f_o = h^2/2md^3$ which
also tries to expand the box. While the relative dynamics of two particles in
their excited states represents usual collisional motion, the same in their
ground state becomes collisionless. These results have great significance in
determining the correct microscopic understanding of widely different many body
systems.
