During this thesis a novel trapping and manipulation technique for neutral atoms on atom chips has been developed and experimentally implemented. Radio-frequency (rf) coupling of internal states of magnetically trapped atoms results in versatile microscopic potentials, which overcome various limitations of static magnetic traps. An extensive experimental analysis of this new technique has been carried out, exploring the state-dependency of the rf potentials and the possible realization of non-trivial trapping geometries. Based on these results, the first coherent matter wave beam splitter on an atom chip has been realized, demonstrating for the first time the all-magnetic coherent splitting of a condensate. This new atom optical tool has then been applied to investigate the phase-properties of one-dimensional Bose-Einstein condensates. The potential configuration developed during this thesis provides direct access to the phase fluctuations in the system and has allowed the first time-resolved study of equilibrium properties and non-equilibrium dynamics in a one-dimensional Bose gas
