  We develop a geometric approach to quantum mechanics based on the concept of
the Tulczyjew triple. Our approach is genuinely infinite-dimensional and
including a Lagrangian formalism in which self-adjoint (Schroedinger) operators
are obtained as Lagrangian submanifolds associated with the Lagrangian. As a
byproduct we obtain also results concerning coadjoint orbits of the unitary
group in infinite dimension, embedding of the Hilbert projective space of pure
states in the unitary group, and an approach to self-adjoint extensions of
symmetric relations.
