  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.
