UNCERTAINTY RELATION IN QUANTUM-MECHANICS WITH QUANTUM GROUP SYMMETRY

The commutation relations, uncertainty relations, and spectra of posit ion and momentum operators were studied within the framework of quantu m group symmetric Heisenberg algebras and their (Bargmann) Fock repres entations. As an effect of the underlying noncommutative geometry, a l ength and a momentum scale appear, leading to the existence of nonzero minimal uncertainties in the positions and momenta. The usual quantum mechanical behavior is recovered as a limiting case for not too small and not too large distances and momenta.