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.

العنوان

Journal of Physics A: Mathematical and General, V. 38, N. 21, 4637

الناشر

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بلد الناشر

فلسطين

نوع المنشور

Both (Printed and Online)

المجلد

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السنة

2005

الصفحات

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