Localization in space for a free particle in ultrametric quantum mechanics

A study was conducted to construct models of quantum dynamics on general ultrametric spaces and prove the localization property for an ultrametric free quantum particle. An ultrametric quantum particle without any group structure and propagating in a generic ultrametric space was considered for the study. The dynamics of the particle was described by the Schródinger ultrametric equation and it was also found that the ultrametricity of the space generated a new phenomena such as a wave packet with mean zero localized at each moment of time. The analysis of ultrametric wavelet and the theory of ultrametric pseudodifferential operators (PDO) were used as main tools to construct the models. Quantum mechanics was studied and a free quantum particle in the ultraistic space was also described in real time.