Abstract:
The mathematical formulation of Bohr's complementarity principle \break leads to the concepts of mutually unbiased bases in Hilbert spaces and complementary quantum observables. We consider the algebraic structures associated with these concepts and their applications to constructive quantum mechanics. Computer-algebraic approaches to the problems under consideration are briefly discussed.
Key words and phrases:complementarity principle, Weyl's canonical commutation relation, complementary observables, mutually unbiased bases, finite quantum mechanics, quantum mereology.