A Noncommutative Approach to Ordinary Differential Equations

Author: F. Bagarello

Source: International Journal of Theoretical Physics, Volume 43, Number 12, December 2004 , pp. 2371-2394(24)

Publisher: Springer

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Abstract:

We adapt ideas coming from Quantum Mechanics to develop a non-commutative strategy for the analysis of some systems of ordinary differential equations. We show that the solution of such a system can be described by an unbounded, self-adjoint and densely defined operator H which we call, in analogy with Quantum Mechanics, the Hamiltonian of the system.

We discuss the role of H in the analysis of the integrals of motion of the system. Finally, we apply this approach to several examples.

Keywords: ordinary differential equations; quantum evolution

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10773-004-7705-4

Affiliations: 1: Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, I-90128, Palermo, Italy, Email: bagarell@unipa.it

Publication date: 2004-12-01