  The ground state of a system of $N$ impenetrable hard core quantum particles
in a 1-D box is analyzed by using a new scheme applied recently to study a
similar system of two such particles {\it [Centl. Eur. J. Phys., 2(4), 709
(2004)]}. Accordingly, each particle of the system behaves like an independent
entity represented by a {\it macro-orbital}, -a kind of pair waveform identical
to that of a pair of particles moving with ($q$, $-q$) momenta at their {\it
center of mass} which may have any momentum $K$ in the laboratory frame. It
concludes: (i) $<A\delta{(x)}> = 0$, (ii) $<x> \ge \lambda/2$ and (iii) $q \ge
q_o (= \pi/d)$ (with $d = L/N$ being the average nearest neighbour distance),
{\it etc.} While all bosons in their ground state have $q = q_o$ and $K = 0$,
fermions have $q= q_o$ with different $K$ ranging between 0 and $K = K_F$ (the
Fermi wave vector). Independent of their bosonic or fermionic nature, all
particles in the ground state define a close packed arrangement of their equal
size wave packets representing an ordered state in phase ($\phi-$)space with
$\Delta\phi = 2n\pi$ (with $n$ = 1,2,3, ...), $<x> = \lambda/2 = d$, and $q =
q_o$. As such our approach uses greatly simplified mathematical formulation and
renders a visibly clear picture of the low energy states of the systems and its
results supplement earlier studies in providing their complete understanding.
