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Ground State of a System of N Hard Core Quantum Particles in 1D Box | Yatendra S Jain
; | Date: |
15 Jun 2006 | Subject: | Soft Condensed Matter | Abstract: | 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) $<Adelta{(x)}> = 0$, (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 $Deltaphi = 2npi$ (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. | Source: | arXiv, cond-mat/0606409 | Services: | Forum | Review | PDF | Favorites |
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