We have investigated the position-dependent dynamics of a trapped ion in a standing wave laser by transforming it to the Jaynes-Cummings-type system under the Lamb-Dicke limit. A variety of novel phenomena are exhibited,e.g. periodic collapse and revival features and long-time scaled revivals of the ionic inversion, depending on its position in the standing wave. Our result provides a way of producing a system equivalent to the two-photon Jaynes-Cummings model in the trapped ion system, with its exact periodicities.