  The quantum mechanics of one degree of freedom exhibiting the exact conformal
SL(2,R) symmetry is presented. The starting point is the classification of the
unitary irreducible representations of the SL(2,R) group (or, to some extent,
its universal covering). The coordinate representation is defined as the basis
diagonalizing the special conformal generator K. It is indicated how the
resulting theory emerges from the canonical/geometric quantization of the
Hamiltonian dynamics on the relevant coadjoint orbits.
