Liouville Integrability of the Schroedinger Equation

Details Liouville Integrability of the Schroedinger Equation Liouville Integrability of the Schroedinger Equation

1997-10-07

arxiv.org/abs/quant-ph/9710022v1

Physics

Quantum Physics

13 pages, Latex, no figures

Scientific paper

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.

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