Simultaneous measurement of coordinate and momentum on a von Neumann latticeA. Mann, M. Revzen and J. Zak
Department of Physics, Technion-Israel Institute of Technology - Haifa 32000, Israel
received 15 May 2008; accepted in final form 24 May 2008; published July 2008
published online 18 June 2008
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 = M1M2, with M1 and M2 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.
03.65.-w - Quantum mechanics.
04.60.Ds - Canonical quantization.
04.60.Nc - Lattice and discrete methods.
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