Ground State of a System of N Hard Core Quantum Particles in 1D Box
Abstract
The ground state of a system of $N$ impenetrable hard core quantum particles in a 1D 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 macroorbital}, 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:condmat/0606409
 Bibcode:
 2006cond.mat..6409J
 Keywords:

 Condensed Matter  Soft Condensed Matter
 EPrint:
 19 pages, no figures