COHERENT STATES IN FINITE QUANTUM-MECHANICS

The ''harmonic oscillator'', introduced by Itzykson and Balian, is con sidered, on finite phase-space lattices with the structure of Galois f ields GF[p2]. We study this system at the classical and quantum mechan ical level. Explicit construction of the quantum eigenstates provides us with a detailed understanding of the spectrum of scales relevant to this model. We construct also the coherent states appropriate to the finite Heisenberg-Weyl and affine groups. Possible applications are di scussed.