Hamiltonian Systems Inspired by the Schrödinger Equation

Details Hamiltonian Systems Inspired by the Schrödinger Equation Hamiltonian Systems Inspired by the Schrödinger Equation

2008-05-27

arxiv.org/abs/0805.4024v1

SIGMA 4 (2008), 046, 9 pages

Physics

Mathematical Physics

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (Ju

Scientific paper

10.3842/SIGMA.2008.046

Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and conservation laws are obtained. Special cases for the free evolution of the wave function with fixed G and the pure dynamics of G are calculated. The usual, first- and second-order modified Schr\"odinger equations are obtained.

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