2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52919A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools embedded in q-deformed and noncommutative quantum mechanics. A rather fundamental approach, called deformation quantization, is noted. A few relations between noncommutativity and nonarchimedean spaces as well as similarities between corresponding quantum theories on them are pointed out. An extended Moyal product in a proposed form of adelic noncommutative quantum mechanics is considered. We suggest some question for future investigations.8 pages, Talk presented at the 8th Adriatic Meeting, "Particle Physics in the new Millennium", (Dubrovnik, Croatia)High Energy Physics - TheoryMathematical Physicstext