Submitted on 19 Jun 2008 (v1), last revised 20 Jun 2008 (this version, v2).-- 20 pages and 1 figure; typos corrected, references addedWe develop a Hamiltonian picture for a family of models of nonrelativistic AdS/CFT duality. The Schrodinger group is realized via the conformal quantum mechanics of De Alfaro, Fubini and Furlan in the holographic direction. We show that most physical requirements, including the introduction of harmonic traps, can be realized with exact AdS metrics, but without any need for exotic matter sectors in the bulk dynamics. This Hamiltonian picture can be used to compare directly with many-body spectra of fermions at unitarity on harmonic traps, thereby providing a direct physical interpretation of the holographic radial coordinate for these systems. Finally, we add some speculations on the dynamical generation of mass gaps in the AdS description, the resulting quasiparticle spectra, and the analog of `deconfining' phase transitions that may occur.This work was partially supported by Spanish Research Ministry, MEC and FEDER under grant FPA2006-05485, Spanish Consolider-Ingenio 2010 Programme CPAN (CSD 2007-00042), Comunidad Autónoma de Madrid, CAM under grant HEPHACOS P-ESP-00346, Spanish Consolider-Ingenio 2010, and the European Union Marie Curie RTN network under contract MRTN-CT-2004-005104. C.A.F. enjoys a FPU fellowship from MEC under grant AP2005-0134.Peer reviewed