A Non-Commutative Approach to Ordinary Differential Equations
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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.
Keywordsordinary differential equations quantum evolution
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