Ciaglia, Florio MariaMarmo, GiuseppeSchiavone, Luca2022-10-032022-10-032018-03-05Ciaglia, F. M., Marmo, G. & Schiavone, L. (2019). From Classical Trajectories to Quantum Commutation Relations. Springer Proceedings in Physics, 163-185978-3-030-24747-8https://hdl.handle.net/10016/35828In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian description because of the Noether theorem and because they are the starting point for the quantization. As a matter of fact many ambiguities arise in each step of such a reconstruction which must be solved by the ingenuity of the theoretician. In the present work we describe geometric structures emerging in Lagrangian, Hamiltonian and Quantum description of a dynamical system underlining how many of them are not really fixed only by the trajectories observed by the experimentalist.25eng© Springer Nature Switzerland AG 2019conference outputFísicahttps://doi.org/10.1007/978-3-030-24748-5_9open access374399Classical and Quantum PhysicsCC/0000032915