Simultaneous measurement of coordinate and momentum on a von Neumann lattice

Abstract

It is shown that on a finite phase plane the $kq$-coordinates and the sites of a von Neumann lattice are conjugate to one another. This elementary result holds when the number $M$ defining the size of the phase plane can be expressed as a product, $M=M_1{M}_2$, with $M_1$ and $M_2$ being relatively prime. As a consequence of this result a hitherto unknown wave function is defined giving the probability of simultaneously measuring the momentum and coordinate on the von Neumann lattice.

Published in EPL 83 (2008) 10007

Cited by in corpus (1)

• von Neumann Lattices in Finite Dimensions Hilbert Spaces