Orthonormal coherent states on von Neumann lattices

An averaging procedure in phase plane is developed leading to orthonormalit y of coherent states on a von Neumann lattice. These states correspond to e ntire unit cells of area IE (Planck constant) in the phase plane and they c an be specified by (mb, n (2 pi)/(b) h), where m and n are integers and b i s a constant related to the spread of the harmonic oscillator ground state. The product of uncertainties for the co-ordinate x and momentum p in these states is very close to (h) over bar. This is by a factor of 2 pi smaller than the unit cell area, and makes it, in principle, possible to measure si multaneously n: and p for the location of a unit cell in the phase plane.