Non-Archimedean quantum mechanics via quantum groups

We present a new non-Archimedean realization of the Fock representation q-oscillator algebras where creation and annihilation operators act on complex-valued functions, which are defined local field arbitrary characteristic, for instance, p-adic numbers. This implies that many quantum models constructed using models, in particular, models. In this framework, we select q-deformation Heisenberg uncertainty relation construct corresponding q-deformed Schrödinger equations. way mechanics is p-deformed mechanics. also solve time-independent equations free particle, particle box. last case, show existence discrete sequence energy levels. determine eigenvalues operator general radial potential. By choosing potential suitable form recover levels q-hydrogen atom.