An-Najah National University

Professor Sami M. AL-Jaber - Physics Department

Editorial Board member of Journal of Modern Physics (JMP). Recipient of PFDP Teaching Excellence Award 2010.

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  • Friday, May 27, 2005
  • Connection between the spectrum and the moments of the ground-state density in N-dimensional space
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  • Abstract. We show that a series of recurrent inequalities derived in N = 3 have the same formal expressions in any dimension N ≥ 2. They are derived from the multipole sum rules, and provide us with upper bounds for the moments of the ground-state density depending only on the lowest multipole excitation energy. These bounds are transformed into approximate recurrent relations by means of an empirical correction factor. The 1/r potential and the harmonic oscillator play a key role in establishing this factor, which is exact for these two potentials by construction. For a large class of potentials, we show that this factor tends to 1 as N → ∞. In such cases, at the large-N limit, the lowest state for each multipole excitation exhausts the sum rule. It thus acquires the characteristics of the one-phonon excitation typical of the harmonic oscillator.

    PACS numbers: 03.65.−w, 03.65.Ge, 02.30.Hq

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Sami Mohammad Jaber
Theoretical Physics
Professor, Theoretical Physics, Physics Department, AN-Najah National UniversityNablus, Palestine.
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