ar X iv : c on d - m at / 0 30 64 28 v 1 1 7 Ju n 20 03 N identical particles under quantum confinement : A many - body dimensional perturbation theory approach
نویسنده
چکیده
Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D → ∞ equilibrium (D) structure, and the normal-mode (D) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hardcore potential.
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تاریخ انتشار 2008