Simultaneous measurement of coordinate and momentum on a von Neumann lattice

Details Simultaneous measurement of coordinate and momentum on a von Neumann lattice Simultaneous measurement of coordinate and momentum on a von Neumann lattice

2008-06-24

arxiv.org/abs/0806.3832v2

Physics

Quantum Physics

Published in EPL 83 (2008) 10007

Scientific paper

10.1209/0295-5075/83/10007

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.

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