2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53001We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment of the usual formalism. In particular, we found explicit connections between quadratic Hamiltonians and Lagrangians, in their commutative and noncommutative regimes. In the quantum case we give general procedure how to compute Feynman's path integral in this noncommutative phase space with quadratic Lagrangians (Hamiltonians). This approach is applied to a charged particle in the noncommutative plane exposed to constant homogeneous electric and magnetic fields.11 pages, to appear in the proceedings of the "Third Summer School in Modern Mathematical Physics" (Zlatibor, August 2004), published by Institute of Physics, Belgrade, 2005High Energy Physics - TheoryMathematical PhysicsQuantum Physicstext