1997/10/07 by G. Vilasi, Vilasi, G.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9710022
13 pages, Latex, no figures
arxiv created 1997/10/07 · arxiv updated 2009/12/01
Canonical coordinates for both the Schroedinger and the nonlinear Schroedinger equations are introduced, making more transparent their Hamiltonian structures. It is shown that the Schroedinger equation, considered as a classical field theory, shares with the nonlinear Schroedinger, and more generally with Liouville completely integrable field theories, the existence of a "recursion operator" which allows for the construction of infinitely many conserved functionals pairwise commuting with respect to the corresponding Poisson bracket. The approach may provide a good starting point to get a clear interpretation of Quantum Mechanics in the general setting, provided by Stone-von Neumann theorem, of Symplectic Mechanics. It may give new tools to solve in the general case the inverse problem of Quantum Mechanics.