Abstract
An averaging procedure in phase plane is developed leading to orthonormality of coherent states on a von Neumann lattice. These states correspond to entire unit cells of area h (Planck constant) in the phase plane and they can be specified by (mb,n 2π/b), where m and n are integers and b is 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 . This is by a factor of 2π smaller than the unit cell area, and makes it, in principle, possible to measure simultaneously x and p for the location of a unit cell in the phase plane.
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