  Our goal is the discussion of the problem of mathematical interpretation of
basic postulates (or `principles') of Quantum Mechanics: transitions to quantum
stationary orbits, the wave-particle duality, and the probabilistic
interpretation, in the context of semiclassical self-consistent
Maxwell--Schr\"odinger equations. We discuss possible relations of these
postulates to the theory of attractors of Hamiltonian nonlinear PDEs and to a
new general mathematical conjecture on global attractors of G-invariant
nonlinear Hamiltonian partial differential equations with a Lie symmetry group
G.
  This conjecture is inspired by our results on global attractors of nonlinear
Hamiltonian PDEs obtained since 1990 for a list of model equations with three
basic symmetry groups: the trivial group, the group of translations, and the
unitary group U(1). We present sketchy these results.
