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arXiv · 0805.4024

Hamiltonian Systems Inspired by the Schrödinger Equation

Vasyl Kovalchuk·Jan Jerzy Slawianowski
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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 Schrödinger equations are obtained.

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Vasyl Kovalchuk, Jan Jerzy Slawianowski. 2008-05-27. Hamiltonian Systems Inspired by the Schrödinger Equation. https://doi.org/10.3842/sigma.2008.046

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