Many-body Dimensional Perturbation Theory for QuantumConfined Systems: Application to Bose-Einstein condensates and quantumnanostructures

Systems that involve N identical, interactingparticles under quantum confinementappear throughout many areas of physics, includingchemical, condensed matter, andatomic physics. In this thesis, we present themethods of dimensional perturbationtheory, a powerful set of tools that uses symmetry toyield simple results for studyingsuch many-body systems. We present a detaileddiscussion of the dimensional continuationof the N-particle Schrodinger equation, the D¿¿ equilibrium structure, andthe normal-mode oscillations of this structure. Weuse the Wilson FG matrix methodto derive general, analytical expressions for themany-body normal-mode vibrationalfrequencies, and we give analytical results for threeN-body quantum-confined systems:the N-electron atom, N-electron quantum dot, andN-atom inhomogeneousBose-Einstein condensate with a repulsive hard-corepotential.