Hamiltonian Systems Inspired by the Schr\"odinger Equation
Mathematical Physics
2008-05-28 v1 math.MP
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.0805.4024,
title = {Hamiltonian Systems Inspired by the Schr\"odinger Equation},
author = {Vasyl Kovalchuk and Jan Jerzy Slawianowski},
journal= {arXiv preprint arXiv:0805.4024},
year = {2008}
}
Comments
This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/