  The main goal of these lectures -- introduction to Quantum Mechanics for
mathematically-minded readers. The second goal is to discuss the mathematical
interpretation of the main quantum postulates: transitions between quantum
stationary orbits, wave-particle duality and probabilistic interpretation.
  We suggest a dynamical interpretation of these phenomena based on the new
conjectures on attractors of nonlinear Hamiltonian partial differential
equations. This conjecture is confirmed for a list of {\it model Hamiltonian
nonlinear} PDEs by the results obtained since 1990 (we survey sketchy these
results). However, for the Maxwell--Schr\"odinger equations this conjecture is
still an {\it open problem}.
  We calculate the diffraction amplitude for the scattering of electron beams
and Aharonov--Bohm shift via the Kirchhoff approximation.
