2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51807In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with noncommutative coordinates is equivalent to another one with commutative coordinates. We found connection between quadratic classical Lagrangians of these two systems. We also shown that there is a subclass of quadratic Lagrangians, which includes harmonic oscillator and particle in a constant field, whose connection between ordinary and noncommutative regimes can be expressed as a linear change of position in terms of a new position and velocity.15 pages, references added, minor corrections, to be published in the Proceedings of the Workshop "Contemporary Geometry and Related Topics", (Belgrade, 2002)High Energy Physics - TheoryMathematical PhysicsQuantum Physicstext